Hey guys,
I have been wondering about this for a long time, and I can't seem to reach a solid conclusion. If temperature of an object is related to the movement of its atoms, then is it true to say that a moving object have a higher temperature?
Hello!
I am currently in grade 12. I really like neuroscience and physics (more towards physics) and would like to pursue them in university. Would it be a good idea to do a physics and neuroscience double major or something? I'm thinking of really trying to combine the two, so that I do physics...
I believe I understand it! Could you please check if I've got it right?
Assume y ∈ im A
then y = Ax = (AVV-1)x
y = AV(V-1x)
since V-1x ∈ Rn, then y ∈ im(AV) and im(A) ⊆ im(AV)
Assume y ∈ im AV
then y = AVx = A(Vx)
since Vx ∈ Rn, then y ∈ im(A) and im(AV) ⊆ im(A)
Therefore im(A) = im(AV).
Homework Statement
[/B]
If A is an mxn matrix, show that for each invertible nxn matrix V, im(A) = im(AV)
Homework Equations
none
The Attempt at a Solution
I know that im(A) can also be written as the span of columns of A.
I also know that AV = [Av1 Av2 ... Avn]
so im(AV) is the span of...
That's not what I originally meant. What you're saying is that the speed of the satellite is too low to stay at orbit at R, and because of that a rocket pointing away from Earth exerts an outward radial force on the satellite to keep it in orbit.
What I meant is the exact opposite. The...
Sorry I may have used the wrong wording. What I meant is that the satellite cannot orbit the earth in a circular trajectory with that V and R, and because of that a rocket it helping it stay in an orbit by exerting a force directed towards the centre of the Earth. So the satellite is not...
Assume that a satellite(mass m) is orbiting the Earth(mass M) at radius R and speed V (the orbit is circular). The satellite is in a position such that the force of gravity exerted on it by the planet is not enough to keep it in orbit. Therefore, the satellite has an engine, which always points...
Thanks a lot! Is this method the same as the methods mentioned by the other members? I fail to see a similarity. If this is a different method, how many ways of finding an the basis of an image are there in total?
I've been reading a book on linear algebra. It talks about finding the the basis of kernel and image of a linear transformation. I understand how to find the basis of the kernel, but I don't understand how to find the basis of the image. Could someone please explain a method of doing it? Thank you!
Is engineering physics a good field? I've heard a lot that they find it hard to find jobs because engineers think of them as physicists and physicists think of them as engineers.
How is the job market? What does an engineering physicist actually do?
Yes that is true. It is a long and tedious process. And I'm assuming that with the knowledge of physics that we currently have, it is very unlikely to publish some paper that will "revolutionize" science. Research right now is more about building on ideas and improving them in my opinion.
I'm a high school student and I've been an intern at a university for a couple of weeks. We do research and things like that in physics and astronomy. I've realized that research is something that takes a long time and is frustrating, but at the end result is usually enjoyable? Is this true...
Many problems in modern science are being solved by computers and not humans (though technically it's the humans that give the task to the computer). If this keeps advancing, would there be anything left for us as a "job?" Sorry if my question sounds dumb but i thought it would be interesting to...
Hi guys!!
I was wondering if there is a generalization to the Fresnel equations. Those equations calculate the reflective and transmissive coefficients, but it depends on the polarization of the incident ray. Is there a formula that could calculate those constants for an unpolarized incident...
well I'd say it means mathematicians don't really care about the solution as long as it exists. They don't solve the problem, they just make sure it has a solution. It's not true in all cases of course.