1. The problem statement, all variables and given/known data Group of rotations of S^1 = SO(2)=S^1 conincidently Group of rotations of S^2 = SO(3) Group of rotations of S^3 = SO(4) Correct? 3. The attempt at a solution SO(3) is the group of all rotations in R^3 so it can rotate all elements of S^2 which is part of R^3. Although I can't show it rigorously. Would it be enough to say since SO(3) consists of all rotations in R^3, it can offcouse rotate all elements having unit distance from the origin. Similar argument made to S^1 and S^3.