2) Three positive charges are located as shown in the diagram below q1 1cm q3 q1 1cm q2 find the size of electrostatic force exerted by charge q3.​

Answers

Answer 1
To find the electrostatic force exerted by charge q3 on charge q1, we can use Coulomb's law:

F = k * (q1 * q3) / r^2

where:

k is Coulomb's constant (8.99 x 10^9 N * m^2 / C^2)
q1 and q3 are the magnitudes of charges 1 and 3 (assumed to be in Coulombs)
r is the distance between the charges (1 cm in this case)
So the force can be calculated as:

F = 8.99 x 10^9 N * m^2 / C^2 * (q1 * q3) / (1 cm)^2

Plugging in the numbers, assuming q1 and q3 are both 1 Coulomb each:

F = 8.99 x 10^9 N * m^2 / C^2 * (1 Coulomb * 1 Coulomb) / (1 cm)^2
= 8.99 x 10^9 N

The electrostatic force between the two charges is 8.99 x 10^9 N.

Related Questions

you got to the edge of the roof of the physics building and throw one of those other physics textbooks straight up with a speed of 15 m/s. how fast will the book be traveling just before it hits the ground 12m blow you

Answers

The book will be traveling at a speed of 15 m/s just before it hits the ground 12 m below you. Due to gravity, the speed of the book will increase as it falls and reach its maximum velocity of around 24.5 m/s just before it reaches the ground.

The book will be traveling at a speed of 15 m/s just before it hits the ground 12 m below you. Due to gravity, the speed of the book will increase as it falls and reach its maximum velocity of around 24.5 m/s just before it reaches the ground.

As the book falls, gravity will accelerate it toward the ground. The acceleration due to gravity, denoted as g, is a constant value of 9.8 m/s2. This means the book's velocity will increase by 9.8 m/s every second. Therefore, the book will reach its maximum velocity of 24.5 m/s after 2.5 seconds. After this point, the velocity will remain constant until it reaches the ground.

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how to determine if the encoded and measured values ​​of a resistor were within the tolerance of one the other?

Answers

The encoded and measured values ​​of a resistor were within the tolerance of one the other is determined by colour code.

What is a resistor?

In both electrical and electronic circuits, resistors can be used in a variety of ways to control the flow of current or to produce a voltage drop. However, the actual resistor must possess some sort of "resistive" or "resistance" value in order to accomplish this.

The larger width tolerance band oriented to the right side of the resistor colour code markings indicates its tolerance. The resistor colour code markings are always read one band at a time starting from the left to the right.

The first digit of the resistance value is identified by comparing the colour of the first band with its corresponding number in the digit column of the colour chart below.

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Which one of the following can be done to shorten the half-life of the radioactive decay of uranium-238? a. oxidize it to the +2 oxidation state b. freeze it c. none of the above d. heat it e. convert it to UF6

Answers

First off, no known chemical, physical, or environmental approach can change the half-life of a radioactive species so option c. is the correct choice.

Additionally, since radioactivity is a nuclear phenomenon and oxidation is a chemical process, the half-life is unaffected by changes in oxidation.

Additionally, we are performing a chemical reaction by converting it to UF6.

Because U-235 has a shorter half-life than U-238 (700 million), UF6 includes a little amount of it (4.7 billion).

Only altering the state of the electrons around the nucleus can change the half-life of radioactive decay. We can alter a radioactive isotope's half-life by only altering the atoms that are bound to it in its immediate surroundings.

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A box of mass m is hung by a spring from the ceiling of an elevator. When the elevator is at rest, the length of the spring is L = 1m.1)As the elevator accelerates upward, the length of the spring will be?a) L < 1 mb) L = 1 mc) L > 1 m

Answers

The spring needs to be stretched further in order to provide the additional upward force needed for acceleration, hence c) L > 1m.

What is elevator acceleration?

If the elevator is stationary or travelling at a constant speed, N = mg.

If the elevator has an upward acceleration, N = mg + ma.

If the elevator has a downward acceleration, N = mg - ma.

Your perceived weight is equal to the normal force.

As a result of the fact that in this instance both the individual and the elevator are initially travelling up at a constant speed before slowing down to rest on a higher floor. The elevator accelerates in a downward direction.

The spring needs to be stretched further in order to provide the additional upward force needed for acceleration, hence L > 1m.

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Humans have used many natural resources to the point of depletion.
They have also caused problems such as desertification and loss of
habitat. What is an example of a sustainable management practice
for natural resources?

Answers

An example of a sustainable management practice for natural resources is the adoption of conservation techniques and sustainable land-use practices, such as agroforestry.

What is agroforestry?

Agroforestry refers to land-use systems and technologies in which woody perennials are intentionally used on the same land-management units as agricultural crops and/or animals in some form of spatial arrangement or temporal sequence.

Other practices include conservation agriculture, and ecologically based pest management, water harvesting and recharge, renewable energy production, reducing waste through recycling and composting, and engaging in sustainable forestry practices.

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does the compound with the molecular formula c5h11no have a spectrum of 1 nmr considering that the ir spectrum shows an absorption of around 3400

Answers

No, the molecular formula C5H11NO does not necessarily have an NMR spectrum of 1.

What is molecular formula?

Molecular formula is a notation system used to represent the chemical elements and their relative ratios that make up a particular compound. It is written as a combination of symbols representing each element in the compound, with subscripts indicating the number of atoms of each element.

An NMR spectrum is determined by the type of nuclei present in the molecule and the environment of those nuclei. In this case, the molecule contains Carbon (C), Hydrogen (H), Nitrogen (N), and Oxygen (O) nuclei, and the IR spectrum shows an absorption at around 3400 cm-1. This could indicate the presence of a C=O bond, which could influence the NMR spectrum. Therefore, it is not possible to determine whether or not the compound has an NMR spectrum of 1 without further information about the structure of the molecule.

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2. How does your model demonstrate the differences between the types of tectonic plates and the resulting observations in the asthenosphere?

3. How did your hypotheses of your Tectonic Egg Model compare to your experimental results?

4. What are some shortcomings of using this model as a replicable of the Earth? Suggest a way that a scientist could create a more accurate model of Earth’s tectonic plates.

Answers

The answers include the following:

The model demonstrates the differences between the types of tectonic plates and in the asthenosphere there are two types of tectonic plates which are oceanic and continental.Hypotheses of your Tectonic Egg Model compare to your experimental results such that the former is denser due to it being formed from silica, magnesium etc. Some shortcomings of using this model as a replicable of the Earth is the absence of various materials and gases and a more accurate model of Earth’s tectonic plates can be done by making it rugged and youthful.

What is Plate tectonics?

This is referred to as a scientific theory that explains how major landforms are created as a result of Earth's subterranean movements.

The Tectonic Egg Model when compared to your experimental results is different such that the former is denser due to it being formed from silica, magnesium etc.

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How do you solve Newton's law of cooling in differential equations?

Answers

Newton's law of cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the temperature of its surroundings. This relationship can be mathematically modeled using a first-order ordinary differential equation.

The general form of the equation for Newton's law of cooling is:

[tex]dT/dt = k(T_s - T)[/tex]

where T is the temperature of the object, [tex]T_s[/tex] is the temperature of its surroundings, k is the constant of proportionality known as the cooling rate, and t is time.

To solve this differential equation, we need to find the function T(t) that satisfies the equation. One method to solve this equation is to use the method of separation of variables. We separate the variables T and t, integrate both sides, and then solve for T.

The solution to this differential equation gives us the time-dependent temperature of the object as it cools down to the temperature of its surroundings. This solution is useful in understanding the cooling process of objects in various real-world scenarios such as heat transfer in electronics, refrigeration, and air conditioning systems.

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A man pushes a lawn mower on a level lawn with a force of 211 N. If 50% of this force is directed forward, how much work is done by the man in pushing the mower 5.7 m?

Answers

Answer:

1201.7 N.m

Explanation:

The amount of work done by the man in pushing the mower 5.7 m can be calculated using the following formula: Work = Force x Distance. Therefore, the amount of work done by the man in this case can be calculated as: Work = 211 N x 5.7 m = 1201.7 N.m.

Consider a planet orbiting the Sun in a noncircular orbit. It will slow down as it journeys away from the Sun and speed up as it moves closer to the Sun. A way of stating this motion is that the planet is______

Answers

A way of stating this motion is that the planet is accelerating towards the Sun and decelerating away from it.

This is because the gravitational force of the Sun is stronger when the planet is closer, and weaker when the planet is further away. As a result, the planet's speed changes as it moves along its orbit.

Planets orbit around the Sun in an elliptical path, which is shaped like an oval. This path is determined by the gravitational force of the Sun on the planet. The closer the planet is to the Sun, the faster it moves, and the further away it is, the slower it moves. This means that the planets can be closer or further away from the Sun depending on their position in their orbit. As the planets orbit the Sun, their distance from the Sun changes, and this causes the seasons on Earth.

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Wind energy is increasingly relied upon to help meet global energy needs. Wind energy can be used to generate electricity using wind turbines. Which of the following are often used for energy storage of wind power? A). Converters B). Generators C). Batteries D). Rotor blades

Answers

Batteries are frequently used to store wind energy.

What is energy?

Energy is a quality of matter and radiation that serves as a gauge of work-doing capacity. It can manifest in a variety of ways, including as electromagnetic radiation, thermal energy, kinetic energy, and more.

It is necessary to store the wind energy produced by wind turbines so that it can be used when there is no generation due to unfavorable wind conditions. The energy produced by wind turbines can be stored in batteries and made available for use as needed. Battery energy can also be utilized to stabilize the power system, increasing its dependability and enhancing the grid's overall ability to integrate wind energy.

a. In order to convert the direct current (DC) electricity produced by wind turbines into the alternating current (AC) electricity that is typically used in homes and businesses, converters are needed.

b. Although they can be used to generate electricity, generators are not typically used in wind power systems for energy storage.

d. Rotor blades, which are a component of wind turbines, are used to collect wind energy and transform it into mechanical energy, which is later transformed into electricity. Energy is not stored in rotor blades.

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a) Work out the value of 2³ + 5²
b) Work out the value of 7^2-3³
c) Work out the value of 8^2+ √100

Answers

a) 2³ + 5² = 33

2³ -> 8
5² - > 25
8 + 25 = 33


b) 7² - 3³ = 22

7² -> 49
3³ -> 27
49 - 27 = 22


c) 8² + √100 = 74

8² -> 64
√100 -> 10
64 + 10 = 74

At what point(s) is the gravitational potential energy (GPE) the greatest?

Answers

Answer:The answer is "when it is in the air" because when objects are positioned higher off the ground they have more gravitational potential energy.

Explanation:

a current of 2 Ampere passes through a wire of resistance 4ohms for 3mins calculate the energy Lost​

Answers

The amount of energy lost is equal to 2880 joules if a current of 2A flows through a wire with a resistance of 4 for 3 minutes.

Given according to the question-

Current passing through the wire (I) = 2A

Resistance of the wire (R) = 4Ω

Time for which the current passed in the wire (t) = 3mins = 3 x 60

sec= 180sec. {converting minutes into seconds}

To be calculated

Energy loss (E)

According to Formulae

The electric energy that an electric current delivers is a function of both its strength and the amount of time it flows, and is thus a function of voltage, current and time.

[tex]E = Pt = VIt[/tex]

In order to create variants, this equation and Ohm's law can be used together.

[tex]E = VIt = I^{2} Rt[/tex]

E =  I²Rt

E = 2² × 4 × 180

E = 2880J

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600 ml of air is at 27c. What is the volume of 60c

Answers

The volume of 60c is 1333.33 ml

How to find the volume

The volume of a gas is directly proportional to its temperature, provided the pressure remains constant. The equation for this relationship is:

V1 / T1 = V2 / T2

where

V1 is the initial volume,

T1 is the initial temperature,

V2 is the final volume, and

T2 is the final temperature.

when V1 = 600 ml and T1 = 27°C, we can solve for V2:

V2 = (V1 * T2) / T1

V2 = (600 ml * 60°C) / 27°C

V2 = 1333.33 ml

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Find the work WAB in electron volts done by the electric force on a proton that moves from point A to point B. Similarly, find WAC, WAD, and WAE. (Assume the proton starts and stops at rest. Enter your answers in eV.)

Answers

The work WAB in electron volts done by the electric force on a proton that moves from point A to point B can be calculated using the equation W = qE, where q is the charge of the proton and E is the electric field at point B.

Similarly, the work WAC, WAD, and WAE can be calculated using the same equation, substituting in the electric field at points C, D, and E respectively.

Assuming the proton starts and stops at rest, the answers in eV will be equal to the product of the proton's charge and the electric field at the respective points.

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One pass traveled 63 yards from quarterback to receiver. The pass was thrown at 45 degree angle, what was the speed at which the ball left the quaterback’s hand?

Answers

The speed at which the ball left the quaterback’s hand was 23.76 m/s.

What is projectile motion?

When a particle is hurled obliquely near the surface of the earth, it travels along a curved path while accelerating continuously in the direction of the planet's centre.

Such a particle's motion is known as projectile motion, and its route is referred to as a projectile.

The range of the pass is = 63 yards = 63 × 0.9144 meter = 57.6072 meter

Angle of projection = 45 °

Acceleration due to gravity =  9.8 m/s²

Hence, the initial speed is =  √{(9.8 ×  57.6072)/sin(2×45°)} m/s

= 23.76 m/s

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A container with volume 1.54 L is initially evacuated. Then it is filled with 0.221 g of N2. Assume that the pressure of the gas is low enough for the gas to obey the ideal-gas law to a high degree of accuracy.
If the root-mean-square speed of the gas molecules is 182 m/s , what is the pressure of the gas?

Answers

The pressure of the gas in a container with a volume of 1.54 L is initially evacuated. Then it is filled with 0.221 g of N2 is 1619Pa.

A gas with a small density and at a sufficiently high temperature so that the interaction between its particles can be neglected can be considered an ideal gas. In this case, the pressure, volume, and temperature of the gas are related as follows:

PV=mMRT, where m is the mass of the gas and M is the molar mass of the gas. The pressure of the gas can be found using the ideal gas law:p =mRT/MV.

The temperature of the gas can be found from the RMS speed of the molecules of nitrogen, which is given by: vrms=√3RT/M. Solving for the temperature, we obtain: T= Mv² / 3 R. And pressure is P= mv² /3V. So P=[ 0.221×(184)²]/ 3×1.54 = 1619 Pa.

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Neglecting friction, if a Cadillac and Volkswagen start rolling down a hill together, the heavier Cadillac will get to the bottom:A. before the Volkswagen.B. at the same time as the Volkswagen.C. after the Volkswagen.

Answers

Answer is B. at the same time as the Volkswagen. Because without friction the mass will have no effect on acceleration.

How acceleration is effected by friction?

According to Newton's second law, an object's acceleration is inversely correlated with its net external force.

We now understand that the net force, also referred to as an unbalanced force, is the vector sum of all the forces that have been applied to the object. We are aware that friction frequently causes motion to go in the other direction. This implies that friction causes a contraction and cancels out some of the force that causes motion.

This suggests a smaller acceleration and a smaller net force.

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A plane flying in a straight line in the sky moves a total of 5100m in one minute ( not in second) How far was it traveling on average?

Answers

Answer:

see below

Explanation:

Distance = 5100m

time = 1min = 60s

avg speed= distance/time

v = 5100m/60s

v = 85m /s

so the plane was traveling a average distance of 85m per second.

EXPERIMEXPERIMENT: SIMPLE MACHINES When we think of a machine, car engines, cranes, lifts, power drills, and vacuum cleaners usually come to mind. These devices are complex machines. Simple machines are the wedge, inclined plane, screw (an inclined plane wrapped on an axle), pulley, and lever. The jack used to lift a car is an example of a simple machine; it is simply a lever. In this investigation you will use a lever as a simple machine, and calculate its mechanical advantage and efficiency. Here are your goals for this lesson: Make quantitative observations and measurements with precision Analyze, evaluate and predict patterns from data Communicate findings These supplies are needed: meter stick string weights Play Mute Remaining TimeÂ-1:08 Picture-in-Picture Follow these directions and complete the activities. 1. Suspend the meter stick by a string from its center. 2. Notice carefully where it balances. It probably will not balance exactly at 50 cm. All distances must be measured to this point (called the fulcrum). 3. Hang a 200 g mass on one side and a 50 g mass on the other and adjust the distances from the fulcrum until the meter stick balances.(Be sure to account for the mass of the hanger from which you are suspending the masses. This can either be part of the total mass or, alternatively, if you are using something like coffee cups to hold the masses, their masses need to be matched perfectly before starting the experiment. You can do this by first checking to see how close they com

Answers

Answer:

This a practical that you have to do. Not to us.

Explanation:

EXPERIMEXPERIMENT: SIMPLE MACHINES When we think of a machine, car engines, cranes, lifts, power drills, and vacuum cleaners usually come to mind. These devices are complex machines. Simple machines are the wedge, inclined plane, screw (an inclined plane wrapped on an axle), pulley, and lever. The jack used to lift a car is an example of a simple machine; it is simply a lever. In this investigation you will use a lever as a simple machine, and calculate its mechanical advantage and efficiency. Here are your goals for this lesson: Make quantitative observations and measurements with precision Analyze, evaluate and predict patterns from data Communicate findings These supplies are needed: meter stick string weights Play Mute Remaining TimeÂ-1:08 Picture-in-Picture Follow these directions and complete the activities. 1. Suspend the meter stick by a string from its center. 2. Notice carefully where it balances. It probably will not balance exactly at 50 cm. All distances must be measured to this point (called the fulcrum). 3. Hang a 200 g mass on one side and a 50 g mass on the other and adjust the distances from the fulcrum until the meter stick balances.(Be sure to account for the mass of the hanger from which you are suspending the masses. This can either be part of the total mass or, alternatively, if you are using something like coffee cups to hold the masses, their masses need to be matched perfectly before starting the experiment. You can do this by first checking to see how close they com

A player hits a ball with a bat. The action force is the impact of the bat against the ball. What is the reaction to this force?A. The force of the ball against the batB. The weight of the ballc. C. Air resistance on the balld. D. The grip of the player's hand against the bate. E. none of the above

Answers

The reaction to this force is A:  "The force of the ball against the bat".

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. When a player hits a ball with a bat, the action force is the impact of the bat against the ball. The reaction to this force is the equal and opposite force of the ball against the bat, meaning the ball will push back against the bat with the same amount of force that the bat hit it with.

So, the force of the ball against the bat is the equal and opposite reaction to the impact of the bat against the ball.

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When infrared radiation is absorbed by a greenhouse gas molocule the infared radiation can never leave earths atmospher. T/F?

Answers

The given statement about “When infrared radiation is absorbed by a greenhouse gas molecule the infrared radiation can never leave Earth atmosphere” is false, because the circulating infrared radiation in the atmosphere will eventually escape into space.

Greenhouse gases are needed in order to maintain a temperature on our planet that is suitable for the continuation of life. Without the natural greenhouse effect, the heat that the Earth radiates into space would simply escape outwards from the surface of the planet, and the average temperature of the planet would be somewhere about -20 degrees Celsius.

Because it emits energy into space as infrared radiation, which is invisible to the human eye, the Earth does not get hotter and hotter as it receives energy from the sun. The Earth must emit an amount of infrared radiation that is equal to the amount of energy that is absorbed from sunlight in order for there to be an energy balance. The temperature of the Earth affects how much infrared radiation energy it emits.

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Which equation represents inverse proportionality?
Responses

y=m/x
y equals m divided by x

y=mx2+b for nonzero b
y equals m x squared plus b for nonzero b

y=mx
y equals m x

y=mx2

Answers

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Inverse proportionality means that the two terms should be proportional to inverse of each other ~

That is :

[tex]\qquad \sf  \dashrightarrow \: y \propto \dfrac{1}{x} [/tex]

And according to given options, only option 1 shows inverse proportionality. where y is inversely proportional to x and m is proportionality constant.

[tex]\qquad \sf  \dashrightarrow \: y = \dfrac{m}{x} [/tex]

Below are the blackbody curves for three different stars.

a.) Rank the temperature of the three stars from hottest to coldest.

b.) Which star will appear reddest? Which star will appear bluest?

Answers

(a) The ranking of the stars from the hottest to coldest is star A , star C and then star B.

(b) The star that will appear the reddest is star C and the star that will appear the bluest is star A.

Which star has the highest temperature?

The star with the highest temperature is determined by based on the energy of the stars.

The star with the highest temperature is ranked as follows;

star Astar C star B

On one end of the spectrum is red light, with the longest wavelength. Blue or violet light has the shortest wavelength. So the star that will appear the reddest is star C and the star that will appear the bluest is star A.

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A 180 kg motorcycle travels in a straight line on a horizontal road. The relationship between motorcycle’s velocity and time are given by the above graph. What is the acceleration during the first 5 s? What is the net force during first 5 s? What is the acceleration from 5 s to 10s? What is the net force from 5 s to 10 s? What is the acceleration from 10 s to 15 s? What is the net force from 10 s to 15 s? What is the acceleration from 15 s to 25s? What is the net force from 15 s to 25 s?A 180 kg motorcycle travels in a straight line on a horizontal road. The relationship between motorcycle’s velocity and time are given by the above graph. What is the acceleration during the first 5 s? What is the net force during first 5 s? What is the acceleration from 5 s to 10s? What is the net force from 5 s to 10 s? What is the acceleration from 10 s to 15 s? What is the net force from 10 s to 15 s? What is the acceleration from 15 s to 25s? What is the net force from 15 s to 25 s?

Answers

Answer:

need points my fault

Explanation:

What did each of the boys add to the success of the science fair win? Would Homer have been able to full-fill his dream without each of his friends or others? - October Sky

Answers

I would have to read the book to help u answer this one

Two identical balls are at rest side by side at the bottom of a hill. Some time after ball A is kicked up the hill, ball B is given a kick up the hill. Ball A is headed downhill when it passes ball B headed up the hill. At the instant when ball A passes ball B, it has the same position and velocity as ball B. Pit has the same position and acceleration as ball B. c. it has the same velocity and acceleration as ball B. d. it has the same displacement and velocity as ball B. e. it has the same position, displacement and velocity as ball B.

Answers

When ball A passes ball B, A's position and acceleration are the same as those of B.

Describe acceleration.

The rate at which velocity changes is called acceleration. Acceleration typically indicates a change in speed, but not necessarily. An item that follows a circular course while maintaining a constant speed is still moving forward because the direction of its motion is shifting.

The motion of an item is related to the forces operating on it by Newton's equations of motion. According to the first law, until a force acts on an item, it will not alter its motion. According to the second law, an object's force is determined by multiplying its mass by its acceleration. The third rule states that when two things come into contact, they exert forces on one another of equal magnitude and opposite direction.

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he video shows a collapsing cloud of interstellar gas, which is held together by the mutual gravitational attractio

Answers

"The video shows a collapsing cloud of interstellar gas, which is held together by the mutual gravitational attraction of all the atoms and molecules that make up the cloud. As the cloud collapses, the overall force of gravity that draws the cloud inward because the strength of gravity follows an inverse square law with distance."

By the power of gravity, which is a natural phenomena, all objects with mass are drawn towards one another. It is most commonly experienced as the weight of objects pulling them toward the Earth’s centre. Gravity is the weakest of the four fundamental forces of nature, yet it is the most dominant force in determining the structure of the universe. It is the reason why planets, moons, and galaxies remain in their orbits.

Gravity is also responsible for the formation of stars and planets, as well as the attraction between objects such as planets and moons. The gravity between two objects depends upon their mass and distance between them. Gravity is an important factor in the motion of all objects in the universe and is directly responsible for the tides, the motion of the planets and their motion around the sun.

The question is incomplete. The complete question is 'The video shows a collapsing cloud of interstellar gas, which is held together by the mutual gravitational attraction of all the atoms and molecules that make up the cloud. As the cloud collapses, the overall force of gravity that draws the cloud inward because ___.'

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Let T R2 5 R2 be a linear transformation that sends the vector u = (5,2) into (2, 1) and maps 0 = (1,3) into (~1,3) . Use properties of a linear transformation to calculate T(Su) =( 25 ), T(_9v) =( T(Su 90)

Answers

To calculate T(Su 90), we use the fact that T is linear, meaning it respects and final answer is T(_9v) = -9*(-1,3) = (-45, 27).

What is the scalar ?

A scalar is a single quantity that has magnitude but no direction. It is typically represented by a real number and is used to measure the magnitude of a physical or mathematical quantity. Examples of scalars include speed, temperature, mass, energy, and volume. Scalars are contrasted with vectors, which have both magnitude and direction.

T(Su) = (25, 5)

T(_9v) = (-45, 27)

T(Su 90) = (-225, -45) with explanation:

To calculate T(Su), we use the fact that T is linear, meaning it respects the distributive, associative, and scalar multiplication properties. Therefore, we can break down the expression into its constituent parts, T(S*u), which can be written as: T(S) * T(u).

Since S is a scalar (90) and u is a vector (5,2), we can calculate T(S) as 90*T(u) and T(u) as (2,1). Therefore, T(S*u) = 90*(2,1) = (180, 90).

To calculate T(_9v), we use the same principle and break down the expression into its constituent parts, T(_9)*T(v). Since _9 is a scalar and v is a vector (1,3), we can calculate T(_9) as -9*T(v) and T(v) as (-1,3). Therefore, T(_9v) = -9*(-1,3) = (-45, 27).

Finally, to calculate T(Su 90), we use the fact that T is linear, meaning it respects.

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