Recent content by Icheb

A stick of 1m in length travels at v = 1/2 c along its axis away from the observer. Question 1: Show that the observer perceives the length of the stick to be shorter without theory of relativity. Calculate the length as perceived by him if he calculates it by the difference in length...

Space ship Alpha travels at t = 0 and v = 4/5 c to the star Sirius which is 8.6 light years away. One year later spaceship Delta starts at v = 9/10 c to the same star. Question 1: When does Delta overtake Alpha, as measured from Alpha's, Delta's and Earth's perspective? Question 2: At which...

Then you need to get out more.

Ok, you heard about Google's Pagerank, and now I'm telling you to forget about it again. Several years ago Pagerank was a huge determining factor in how websites were ranked, but this is not so anymore! The quality of the link is much more important, making Pagerank as a quantifier of a...

Light is falling on the planar side of a thin planar convex glass lens. The curvature radius |r| is 50cm. I have to calculate the distance of the focal point to the curved surface of the lens, which to my understanding is the focal length, since it's a thin lens. Additionally I am supposed to...

There is a woman who is 1,75m tall standing in front of a mirror. Her eyes are to be 10cm below the top of her head. I have to find out how small the mirror can be so that she can still see her entire body in it and how high it has to be hanging on top of the floor. Now I think I can solve it...

Wouldn't the resulting matrix be of type 4x4? Here's what I found for that scenario: 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0

I figure I'd have to "invent" a solution and then find a B that's based on that? I just have no idea how that would work.

I have the following linear transformation http://img162.imageshack.us/img162/3306/hammingcodeex4.gif with G being a generating matrix for a hamming code and I have to find a matrix B so that the following: \delta \cdot\gamma(\upsilon) = \upsilon for all \upsilon \in Z^4_2 is true for the...

Alright, thank you very much. :)

But why wouldn't it suffice if I assume one element of the main diagonal to be 0, then I use Gaussian transformation to change the last line so it contains only 0s? Then if the last line contains only 0s the determinant would be 0 because of the linearity.

Ok, do I understand it correctly that if all elements of one line equal 0, the determinant equals 0? So I would just have to prove that the matrix is linear (Did I translate that word correctly?) and my proof would be complete? Or am I missing something?

I have a square triangular matrix with d_{ij} = 0 for all 1 \le j < i \le n. Now I have to prove that this matrix is only then invertible when d_{ii} \ne 0 for all 1 \le i \le n. From what I know a matrix is only then invertible when its determinant does not equal 0. I also think that the...

I have a constant magnetic field pointing in the direction of the z axis and I'm supposed to find a formula for the way an electron with arbitrary starting position and velocity would travel in this field. The formula in this case would be F(x, x', t) = q(v × B(x, t)) and I'm stuck at the...

A sphere is submerged half way in water and pulled out at a constant speed. Now I have to find out the average volume of the part of the sphere that is under water. The volume formula would be 4/3 \pi r^3, now the part of the sphere that is under water at first would be 2/3 \pi r^3...