Which of the following are linear transformations from $R{R}^{2}\to R{R}^{2}?$

(d) Rotation: if $x=r\mathrm{cos}\theta ,y=r\mathrm{sin}\theta ,$ then

$\overrightarrow{T}(x,y)=(r\mathrm{cos}(\theta +\phi ),r\mathrm{sin}(\theta +\phi ))$

for some constants $\mathrm{\angle}\phi $

(f) Reflection: given a fixed vector $\overrightarrow{r}=(a,b),\overrightarrow{T}$ maps each point to its reflection with

respect to $\overrightarrow{r}\overrightarrow{T}(\overrightarrow{x})=\overrightarrow{x}-2{\overrightarrow{x}}_{r\perp}$

$=2{\overrightarrow{x}}_{r}-\overrightarrow{x}$