Answer:
Given a set of vectors, you can determine if they are linearly independent by writing the vectors as the columns of the matrix A, and solving Ax = 0.
Explanation:
You may verify if a group of vectors is linearly independent by expressing the vectors as columns of the matrix A and solving Ax = 0.
What is a vector?A vector is a quantity or phenomena with magnitude and direction that are independent of one another. The phrase also refers to a quantity's mathematical or geometrical representation.
If no vector can be written as a linear combination of the others, a set of vectors is said to be linearly independent.
If no vector in a collection of vectors can be written as a linear combination of the ones mentioned before it, the set is said to be linearly independent.
A nontrivial linear combination yields the zero vector, the vectors are said to be dependent.
You may verify if a group of vectors is linearly independent by expressing the vectors as columns of the matrix A and solving Ax = 0.
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20. Free-Body Diagram You are sitting in the back seat of a
car going around a curve to the right. Sketch motion
and free-body diagrams to answer these questions:
a. What is the direction of your acceleration?
b. What is the direction of the net force on you?
Centripetal acceleration
#1
Direction towards centre#2
Direction of force also towards centre
What is the Atomic Mass / Weight for silver? *Round your answer to the nearest whole number
A net constant force of 1500 n gives a toy rocket an acceleration of 2. 5 m/������ 2. What is the mass of the rocket?
Answer:
600Kg
Explanation:
Force= mass × acceleration
mass= 1500/2.5
600kg
The mass of the rocket will be 600 kg.In the International System of Units (SI), the kilogram is the unit of mass.
What is mass?Mass is a numerical measure of inertia, which is a basic feature of all matter. It is, in effect, a body of matter's resistance to a change in speed or position caused by the application of a force.
In the International System of Units (SI), the kilogram is the unit of mass.
The given data in the problem is;
The net constant force is, F= 1500 N
The acceleration is,a=2. 5 m/s²
The mass of the rocket is,m=?
[tex]\rm F= mass \times acceleration \\\\ m = \frac{F}{a} \\\\ m= \frac{1500}{2.5}\\\\ m = 600 \ kg[/tex]
Hence the mass of the rocket will be 600 kg.
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1. A hockey puck has a mass of 0.115-kg and strikes the pole of the net at (37 m/s)x. It bounces off in the opposite direction at (-25 m/s)x +(5 m/s)y. (A) What is the impulse on the puck? (B) If the collision takes .005s what is the force acted on the puck?
(a) The impulse on the puck is 1.323 kgm/s.
(b) The magnitude of the force that acted on the puck is 264.5 N.
Impulse of the puckThe impulse on the puck is equal to the change in momentum of the puck.
The change in th momentum of the puck is calculated as follows;
ΔP = m(u - v)
where;
v is the final velocity = (-25x + 5y) m/su is the initial velocity = 37 m/sMagnitude of the final velocity
|v| = √[(-25)² + (5)²] = 25.5 m/s
ΔP = 0.115(37 - 25.5)
ΔP = 1.323 kgm/s
Thus, the impulse on the puck is 1.323 kgm/s.
Force on the puckThe magnitude of the force that acted on the puck is calculated as follows;
F = ΔP/t
F = 1.323/0.005
F =264.5 N
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What increases the transfer of the wind's energy to the water?
Question 4 options:
A. flat water
B. large waves
C. large rocks
PLEAS HELP ME FAST
Answer:
A, flat water
Explanation:
If the barge is made out of 4.8- cm -thick steel plate on each of its four sides and its bottom, what mass of coal can the barge carry in freshwater without sinking
The maximum mass of coal that the barge will carry in freshwater without sinking is 0.111 kg.
Volume of the bargeThe volume of the barge is calculated as follows;
V = L³
V = (4.8 cm)³
V = 110.6 cm³
Density of the bargeFor the barge to float in freshwater, its density must be less or equal to density of water.
density(barge) = density(water)
density(barge) = 1 g/cm³
Maximum mass to be carried by the barge without sinkingmass = density x volume
mass = 1 g/cm³ x 110.6 cm³
mass = 110.6 g
mass = 0.111 kg
Thus, the maximum mass of coal that the barge will carry in freshwater without sinking is 0.111 kg.
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why did united states withdraw from vietnam war
the Army had a fight in unfamiliar territory but with the combination of disadvantages and a loss of public support what to the United States withdrawing from Vietnam
Explanation:
I hope this helps
Which planets are generally referred to as the ice giants?.
Answer:
The correct answer is Uranus and Neptune
What is one time constant of a 4. 7 μf capacitor in series with a 22 kω resistor?
Hi there!
We can solve for the time constant using the following:
[tex]\tau = RC[/tex]
τ = Time Constant (s)
R = Resistance (Ω)
C = Capacitance (F)
Simply plug in the values. Remember that:
4.7 μF = 4.7 * 10⁻ ⁶ F = 0.0000047 F
22kΩ = 22 * 10³ Ω= 22000Ω
Solve:
[tex]\tau = 0.0000047 * 22000 = \boxed{0.1034 s}[/tex]
Which Tesla would win in a drag race?
(A) 2009 Tesla Roadster
(B) 2016 Tesla Model X
Answer:B
Explanation:
A has about 248 hp but B has about 683 hp. 2016 is younger too. good day
Scientists observed a rocky, rotating object orbiting in space. It was 250 km wide. The rocky object was located several times farther away from the sun than the earth
The rocky object orbiting in space is most likely referred to as an asteroid.
What is an Asteroid?This is referred to a rocky object which revolve around the sun and are considered too small to be called a planet.
Asteroids was observed with the use of a telescope and is around 250 km wide thereby making it the most appropriate choice.
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Which of the following was correctly predicted by Einstein's theory of gravity?
(A) the origin of mass
(B) law of refraction
(C) the measure of G
(D) light deflected around large objects because of their gravity
Answer:
(D) light deflected around large objects because of their gravity
I hope this helps you
:)
What is the difference between gravity and acceleration?
Aceleration refers to motion but gravity refers to force
Acceleration is change of velocity with time while gravity is the force of attraction pulling objects. When this force pulls an object it tends to move with a certain type of acceleration called acceleration due to gravity. This is equal to 9.8 m / s^2 for earth
Acceleration is the rate of change in velocity. While g is the acceleration due to gravity. The pace at which a body's velocity varies is represented by acceleration, which is a vector quantity.
What is acceleration?The rate of change of velocity with respect to time is known as acceleration. According to Newton's second law, the eventual effect of all forces applied to a body is its acceleration.
[tex]\rm a = \frac{v-u}{t}[/tex]
u is the initial speed
v is the final speed
t is the time interval
a is the acceleration of the ball
Gravitation is a natural law by which all things with all matter are attracted towards one another.
g is the acceleration due to gravity. whose value is equal to 9.81 m/sec².The value of the gravitational acceleration varies according to the height and the planet.
The value of the gravitational acceleration on the earth is 9.81 m/sec².While the value of g at the moon is 1.6333 m/sec².
Hence acceleration is the rate of change of velocity. While g is the acceleration due to gravity.
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How many stars are in a typical spiral galaxy, like our own?.
Answer:
200 billion to 400 billion stars in a typical spiral
Explanation:
hope this helps
have an awesome day -TJ
A person is dragging a packing crate of mass 100 kg across a rough horizontal floor where the coefficient of kinetic friction is 0. 400. He exerts a force f sufficient to accelerate the crate forward. At what angle above horizontal should his pulling force be directed in order to achieve the maximum acceleration?.
For a person dragging a packing crate of mass 100 kg, the angle above the horizontal is mathematically given as
theta = 21.8 °
What angle above horizontal should his pulling force be directed in order to achieve the maximum acceleration?.Generally, the equation for the Force is mathematically given as
[tex]Fnet = F_{costheta} - F_{friction}[/tex]
Therefore
Fnet = Fcostheta - mu*((mg) - Fsintheta)
sin theta = mu*costheta
mu = tantheta
theta = tan^-1(mu)
theta = tan^-1(.400)
theta = 21.8 °
In conclusion, the angle above horizontal
theta = 21.8 °
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Write an expression for the coefficient of kinetic friction between the block and the horizontal surface. Your answer should be in terms of x, vB, and g (the acceleration due to gravity)
An expression for the coefficient of kinetic friction between the block and the horizontal surface is given as μk = Ff/mg.
What is coefficient of kinetic friction?
The coefficient of kinetic friction is the force of frcition between a moving object and the horizontal surface.
The expression for the coefficient of kinetic friction between the block and the horizontal surface is given as;
Ff = μkFₙ
Ff = μkmg
μk = Ff/mg
where;
μk is the coefficient of kinetic frictionFf is the kinetic frictional forcem is mass of the blockg is acceleration due to gravityThus, an expression for the coefficient of kinetic friction between the block and the horizontal surface is given as μk = Ff/mg.
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What causes changes in the orbit of objects in the solar system.
A photon with wavelength 11. 0 nm is absorbed when an electron in a three-dimensional cubical box makes a transition from the ground state to the second excited state
For a photon with wavelength 11. 0 nm, the side length LL of the box is mathematically given as
L=1.414*10^{-27}m
What is the side length LL of the box?Generally, the equation for the change in energy is mathematically given as
[tex]dE=\frac{hc}{\lambda}[/tex]
Therefore
[tex]\frac{hc}{\lambda}=\frac{6h^2}{8ml}\\\\L=\sqrt{6h\lambda}{8mc}\\\\L=\sqrt{\frac{6(6.626*10^{-34})*11.0*10^{-9}}{8(9.11*10^31)(3*10^8)}}[/tex]
L=1.414*10^{-27}m
In conclusion, the side length LL of the box is
L=1.414*10^{-27}m
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The side length of the box for a photon of wavelength 11. 0 nm will be [tex]\rm L = 1.414 \times 10^{-27}[/tex] m.
What is wavelength?The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.
The change in the energy of the photon is found as;
[tex]\rm dE = \frac{hc}{\lambda} \\\\ \frac{hc}{\lambda} =\frac{6h^2}{8ml} \\\\ L= \sqrt{\frac{6h\lambda}{8mc} } \\\\ L = \sqrt{\frac{6 \times 6.626 \times 10^{-34}\times 11 \times 10^{-9}}{8 \times 9.11 \times 10^{31} \times 3 \times10^8} } \\\\ L= 1.414 \times 10^{-27} \ m[/tex]
Hence the side length of the box for a photon of wavelength 11. 0 nm will be [tex]\rm L = 1.414 \times 10^{-27}[/tex] m.
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A bicycle wheel of radius 40. 0 cm and angular velocity of 10. 0 rad/s starts accelerating at 80. 0 rad/s2. What is the centripetal acceleration of the wheel at this time point?
The magnitude of the centripetal acceleration of the bicycle wheel is 40 m/s².
Centripetal acceleration of the wheel
The centripetal acceleration of the bicycle wheel is the inward or radial acceleration of the bicycle on the circular path.
The magnitude of the centripetal acceleration of the bicycle wheel is calculated as follows;
a = ω²r
where;
ω is angular speed
r is the radius of the circular path
a = (10)² x 0.4
a = 40 m/s²
Thus, the magnitude of the centripetal acceleration of the bicycle wheel is 40 m/s².
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The acceleration of a body travelling in a circular route is known as centripetal acceleration. The centripetal acceleration of the wheel at this time point is 40 m/sec².
What is centripetal acceleration?The acceleration of a body travelling in a circular route is known as centripetal acceleration. It is given by the formula,
[tex]a_c = \dfrac{v^2}{r} = \omega^2 r[/tex]
The centripetal acceleration of the wheel with angular velocity 10 rad/sec and velocity 40cm (0.4 m) can be written as,
[tex]a_c = \omega ^2\times r\\\\a_c = (10)^2\times 0.4\\\\a_c = 40\rm\ m/sec^2[/tex]
Hence, the centripetal acceleration of the wheel at this time point is 40 m/sec².
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Why wouldn’t you move during an earthquake?
Answer:
So you maybe don't fall, have something fall on you, and for a bunch of different reasons. EARFQUAKES are really dangrous.
Explanation:
Hope this helps you!
2. What would be the effect on your body if you did not have kidneys? Page
112
A. My body would not absorb nutrients.
B. Waste would collect in the blood and become toxic
C. I could not eat gluten
D. Saliva could not be produced
Answer:
b
Explanation:
the kidney eliminates waste from the blood hence no kidney will result in accumulation of waste
A laser beam is used to levitate a metal disk against the force of earth's gravity.
(a) derive an equation giving the required intensity of light, i, in terms of the mass m of the disk, the gravitational acceleration g, the speed of light c, and the cross-sectional area of the disk a. assume the disk is perfectly reflecting and the beam is directed perpendicular to the disk. (do not substitute numerical values; use variables only.)
i =
(b) if the disk has mass 3.89 g and radius 2.40 cm, find the necessary light intensity.
(c) give two reasons why using light pressure as propulsion near earth's surface is impractical.
The necessary light intensity of the disk if the disk has mass 3.89 g and radius 2.40 cm is 6.483 x 10^12cd.
Calculations and Parameters:a. Given that:
i= intensity of light m= mass of disk g= gravitational acceleration c= speed of light a= cross-sectional area of the diskI = P/A
= Force x Speed/Area
Gravitational force, F= GM1M2/r^2
F= ma, F= mg
I= mg x c/q
That is,
i= mass x gravitational acceleration x speed/area
b.
Mass= 3.89g
Radius, r= 2.40cm
i=?
i= mg x c/a
Speed of light= 3.0 x 10^8 m/s
Area, a= /pi r^2
= 3.142 x (0.024)^2
= 3.142 x 0.000576
= 0.0018m^2.
i= 3.89 x 10 x 3.0 x 10^8/0.0018
i= 6.483 x 10^12cd.
c. Light has no mass, therefore, it lacks momentum and cannot exert pressure for propulsion of materials.
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Brody drives 180 km in two hours. How fast is he travelling?
should be in km/hour)
Answer:
90 km/h
Explanation:
we just divide the distance by the time to get the speed.
By what means can the internal energy of a closed system increase?.
Answer:
when work is done on the system or heat comes into the system
Find the number of permutations when 7 objects are taken 1 at a time
Using the formula for permutation, there are 5040 ways that 7 objects are taken 1 at a time.
What is permutation?The permutation of objects refers to the number of ways that an object can be selected from a number of objects.
Given that;
nPr = n!/(n - r)!
Hence;
7P1 = 7!/(7 - 1)!
7P1 = 7 * 6 !/6!
7P1 = 7 * 6 * 5 * 4 * 3 * 2 *1
7P1 = 5040
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Question 3
The FRC robot is rushing to pick up a game ball to shoot. The robot
is at rest and then it travels 30m in 1.96s. What is the robot's
acceleration in this time?
Answer:
15.61 m/s^2
Explanation:
From 3 rd equation of motion
s=ut+1/2at^2
given s = 30
u= 0 ( as body was at rest)
t= 1.96s
30=0*1.96+1/2a(1.96)^2
30=0+1/2a(1.96)^2
a=2*30÷(1.96)^2
a= 15.61 m/s^2 (approx)
Use F = 1/T as your basis:
8. If your heart rate is 150 beats per minute during strenuous exercise, what is the time per beat in units of seconds?
The answer is 0.400 s/beats but please show your work.
Heart rate is given by
150beats/minConvert to per second
150/60=5/2=2.5beats/sNow
Frequency:-
[tex]\\ \rm\rightarrowtail \nu=\dfrac{1}{T}[/tex]
[tex]\\ \rm\rightarrowtail \nu=\dfrac{1}{2.5}[/tex]
[tex]\\ \rm\rightarrowtail \nu=0.4Hz[/tex]
A ball that has a mechanical energy of 65 J haas 10 j of kinetic energy. The ball has j of potential energy
Answer:
55 j
Explanation:
Mechanical energy = kinetic + potential
65 = 10 + P.E.
55 j = PE
What is current of 12 ohm? help me pleasee
Answer:
the current of 12 ohm is 2Amps
Two pistons are in an enclosed volume with fluid in between them, such that
movement in one piston affects the location of the other piston, as shown in
the image below. If an explosion occurs in the piston on the left such that it
moves 1 m, what is the distance that the piston on the right will move
(assuming that friction can be neglected)? (Recall that work on an object is
equal to the force on the object times the distance it is moved, and that work
is conserved.)
Cross-sectional area - 25 mm
Cross-sectional area = 0,5 m
A. 2 m
B. 0.5 m
C. 1 m
D. 0.25 m
Answer:
The pressure in the fluid just below Piston 1 is
p_1=F_1/A_1=361\text{ Pa}.p
1
=F
1
/A
1
=361 Pa.
The pressure in the fluid just below Piston 2 is the same according to Pascal's law:
p_2=p_1=361\text{ Pa}.p
2
=p
1
=361 Pa.
The force being exerted on Piston 2 to keep the two pistons in equilibrium is
F_2=p_2A_2=330\text{ N}.F
2
=p
2
A
2
=330 N.
Explanation: