Which of the following transform as components of a 2d vector?

briteliner
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Homework Statement




which of the following pairs of quantities transform under rotations of the axes as the components of a two-dimensional vector?
a) (x2, -x1)
b) (x2,x1)
c) ((x1)^2,(x2)^2)

Homework Equations





The Attempt at a Solution


Dont know where to start. i'd appreciate just a little guidance :)
 
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I'm not quite sure what you mean by that. If you mean does the transformation L((x1,x2))=(x2,-x1) (for a)) correspond to a rotation by some angle theta, look at the formula in your other post and see if it corresponds to some value of theta.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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