For φ in [0, 2pi) and (x1, x2) in R2 we define a transformation.
R(φ):R2 ---> R2
x ---> R(φ)x=y=(y1,y2)
ie. R(φ) leaves the euclidean norm invariant.
Now geometry isn't my strong point to start with but I usually grasp the topics enough to do the homeworks well, but this may as well be in dutch for as much as I can figure out what to do. We haven't done anything even remotely similar in class and I'm at a loss as to where to even start. I would be really really grateful if someone could help me out a little. Thanks