1. Positive Definite Matrix - I think this is correct? Just want reassurance.

Ah yes, thank you. Just to check quick then I get (x_{1}+bx_{2})^{2}+(4-b^{2})x^{2}_{2} Which is positive when -2\leq b \leq 2, correct? Thanks again.
2. Positive Definite Matrix - I think this is correct? Just want reassurance.

Homework Statement For what b is the following matrix positive definite? (\stackrel{1}{b} \stackrel{b}{4}) (Sorry for the strange way I have that matrix represented) Homework Equations For a positive definite matrix x^{T}Ax for all nonzero x in \Re^n The Attempt at a Solution x^{T}Ax =...
3. What's a good home built gift for an aerospace engineer?

Hi, I've got a friend who's birthday is coming up. She's an aerospace engineer and I was thinking it would be fun to build a small project for her but I'm not sure what. I want it to be specifically aerospace related. I've seen designs for how to build a pocket jet engine, but I wasn't so...
4. How are the percentage contents of the universe calculated?

Thanks for the reply. You explained everything very well, however, I still would like to find the gory details even if they are not very nice to someone who wants to view them. Again thank you.
5. How are the percentage contents of the universe calculated?

Specifically I'd like to know about dark energy. How do we know it's 74% of the universe? I'm really looking for a specific explanation/derivation. I've searched a few places and all I've found so far has been people who say "due to Friedmann's equations" or "the WMAP measurements show that"...
6. Space Station Vs. Moon Base

Like I was saying before, I thought one advantage was that they wouldn't have to have the station change it's path to avoid junk every couple of months like they do with the ISS. I was just asking if the main reason was that it required so much energy. And Nabeshin, apparently they are...
7. Space Station Vs. Moon Base

Why is the idea of putting a station in orbit more appealing then putting on on the moon? I understand the want to test things in low gravity. But what about cost wise? I know that the ISS has to change it's direction every now and then to avoid random junk floating in space, and I understand...
8. Why does zero viscosity allow superfluids to climb?

I had heard that if the container was not sealed the superfluid would move into a lower container. So I figured that meant it must not require there to be the substance on the sides of the container in the first place allowing it to climb up. However, I may have just heard wrong or where I...
9. Why does zero viscosity allow superfluids to climb?

Since there are no frictional forces acting on the superfluid my intuition would tell me that there is no way for the liquid to "climb" the sides of a container. Obviously though, intuition isn't the best thing to go by when it comes to superfluids. I'm just wondering: what mechanism drives it...
10. Need Suggestions For An Experiment - Upper Division Undergraduate

Well I tried to convince the professor to let me do something with simple nuclear fusion, but he thought that too big of a project for the ten weeks. I think we've pretty much decided on the sonoluminescence because of it's awesomeness. I'm doing a physics degree because I want to learn about...
11. Need Suggestions For An Experiment - Upper Division Undergraduate

Hello, During the spring semester of school that is just beginning I will be a junior in physics at the University of Minnesota. I'm taking a physics class called Methods of Experimental Physics II in which for the majority of the semester groups of two will be working on an approved...
12. Why doesn't the asteroid belt block our view of the jovial planets?

Why doesn't the asteroid belt block our view of the jovial planets? I'm assuming it's because the asteroids are just too few, far apart, and small to affect our view, but I'm not sure and I'd like to know. Thanks!
13. Why Dark Matter and Dark Energy?

Yah, that's kind of what I assumed but I wasn't sure how much we really knew. I figured there was good reason for the hype. Thanks much.
14. How Do You Find A Central Force Orbit?

Oops, sorry for never replying. I got caught up with work on other things and haven't visited physics forums for a bit. We were doing some things involving orbits in central force (not necessarily closed) in my mechanics class and I had posted this originally to see if I could get a way to...
15. How Do You Find A Central Force Orbit?

If you are given a central force field and an initial velocity of a particle in this field, how would you go about finding the orbit of the particle in polar coordinates? Thanks for you help and time.