Stretching_Contraction_are_Linear

Let $s_\beta: \R^2 \to \R^2$ be a similarity of $\R^2$. Then $s_{-1}$ is the same as the rotation $r_{\pi}$ of the plane about the origin one half turn. If $\beta \ge 1$, then $s_\beta$ is called a '''stretching''', and if $0 < \beta \le 1$, $s_\beta$ is called a '''contraction'''. If $\beta < 0$, then $s_\beta$ is a stretching or contraction followed by a rotation one half turn. It is also the same as a rotation one half turn followed by a stretching or contraction.