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1. ### How to prove that something transforms like a tensor?

Homework Statement I have several problems that ask me to prove that some quantity "transforms like a tensor" For example: "Suppose that for each choice of contravariant vector (a vector) A^nu(x), the quantities B_mu(x) are defined at teach point through a linear relationship of the form...
2. ### Work and isothermal compressibility

Actually I have one more question. When I do the integration by parts for -PdV I get -(PV-∫VdP). The first term in that equation should be evaluated at the limits 1 and 1000 Pa right? So I put V in terms of P, but then the P's cancel out (V=nRT/P) and there's nothing to evaluate. Is that right?
3. ### Work and isothermal compressibility

Okay, I think this gives me enough to work on. Thanks.
4. ### Work and isothermal compressibility

I assume isothermal compressibility is just how easy or hard it is to compress something at constant temperature. Can I integrate the equation for the compressibility? I'm not sure if you're allowed to separate dV and dP when they're partials at constant T. Like I said, I'm not comfortable with...
5. ### Work and isothermal compressibility

Homework Statement 1 kg of water is at room temperature and the pressure is isothermally increased on the system from 1 atmosphere to 1000 atmospheres. What is the work done? What is the change in heat? What would be the temperature change if this was done adiabatically? The volumetric...

7. ### Projectile motion- solve for initial velocity

I'd say step back and think about what you're trying to solve for. You want v0. So you have two unknowns really: time and the initial velocity. When you have two unknowns you're going to need two equations that involve those two unknowns to solve for them both. You're making things more...
8. ### Projectile motion- solve for initial velocity

You're definitely on the right track, but vf2 doesn't involve time, does it? Basically, you've solved for the time it takes for the ball to go 20 meters with initial velocity v0. Now, you also know that the ball has to travel 5 meters vertically in that same amount of time. Can you use that...
9. ### Statistical Mechanics Mean Field Model

I don't think I've fully grasped the underlying ideas of this class, so at the moment I'm just sort of flailing for equations to plug stuff into... Homework Statement Show that in the mean field model, M is proportional to H1/3 at T=Tc and that at H=0, M is proportional to (Tc - T)1/2...
10. ### Linearity in differential equations

Okay, then my book's answer key is wrong. Thanks.
11. ### Linearity in differential equations

Fair enough, but if y is the function then x is the independent variable, right?
12. ### Linearity in differential equations

Homework Statement Is the equation (x2sinx + 4y) dx + x dy=0 linear This problem also asks me to solve it, but I don't have a problem with that part. Homework Equations An equation is linear if the function or its derivative are only raised to the first power and not multiplied by each other...

Right, x=0 .
14. ### Need some guidance on Linear Algebra proofs

Okay, I'll give it one more go... ad-bc=0 Ax=0 if we plug <-b,a> for x we get, a(-b)+b(a)=0 and c(-b)+d(a)=0, which is ad-bc=0 so ad-bc=ad-bc when x=<-b,a>?
15. ### Need some guidance on Linear Algebra proofs

Yeah, I think this is some of the essential kind of information I'm missing. These kind of logic statements are pretty foreign to me, so I don't actually know the difference between p implies q and q implies p. They look like they mean the same thing to me.
16. ### Need some guidance on Linear Algebra proofs

So, we showed that ad-bc=0 if <-b, a> is a solution, and that also <0, 0> is a solution?
17. ### Need some guidance on Linear Algebra proofs

Okay, let me see if I can follow what's going on here, because I think there's a lot that's implied but not stated outright. I'm trying to show that when ad-bc = 0 there's more than one solution for x in Ax=0. We splitting it up into two different scenarios, on where a and b are zero and one...
18. ### Need some guidance on Linear Algebra proofs

I get all that. That's just algebra with matrices and vectors. Could I have just said that when ad-bc=0 that the inverse is undefined because 1/0 is undefined?
19. ### Need some guidance on Linear Algebra proofs

wabbit: Sorry, I don't actually understand the meaning of what you've written. "iff" is if and only-if, which I remember from CS 101, and we just learned about maps being matrix transformations(?), but I don't follow v--> Av. vela: Theorem 5 in my book says that Ax=b (it drives me a little...
20. ### Need some guidance on Linear Algebra proofs

Maybe. A matrix is invertible if it only has the trivial solution?
21. ### Need some guidance on Linear Algebra proofs

I'm getting stuck on the logic portion of it. I can multiply it out, but why does that prove it's not invertible. More importantly why did they pick (-b and a) to be the entries for x2 in the first place? Yes, I know the hint says to do it, but why?
22. ### Which constants to use in Saha Equation

Sorry it's (1/(m2))3/2
23. ### Which constants to use in Saha Equation

It's been a while since I had Stellar Astrophysics, but let's see: mass of the electron should be in eV/c2 (I like eV better than SI units) k is eV/K T is K h is eV⋅s so that's eV/c2⋅eV/K⋅K/(eV⋅s)2 all to the 3/2 looks like everything cancels except c2 and s2, but c2=m2/s2 so all you're left...
24. ### Need some guidance on Linear Algebra proofs

First, let me say that I am a senior physics undergrad. I have failed Linear Algebra once before. Otherwise I am a straight A student. I'm also taking Ordinary Differential Equations right now, and I breeze through that class without a care in the world. I'm not sure if I've developed some sort...