A geometric linear transformation transforms the point P(x;y) into the point P'(kx;ky): S is a homothety with center at O.
A geometric linear transformation rotates the point P(x;y) by an angle α: R is a rotation with center at O.
Rotations transform the segments into segments with equal length: therefore they are isometries.
The composition of a rotation with a homothety is a similarity with center at O: