The only examples I've found are either very complicated, or state the transformation like y=g(u,v) x=f(u,v), whereas this question states u and v in terms of x and y.
I'm not sure how to get started. If I use F to solve for x and y in terms of u and v, sqrt($x^{2}+y^{2}$) will still have a y in it, and vice versa.
Hint: Convert the coordinates into polar form.