\(= \begin{pmatrix} k & 0 \\ 0 & k \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}\)
\(= \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & cos\theta \end{pmatrix} \begin{pmatrix} x-a \\ y-b \end{pmatrix} + \begin{pmatrix} a \\ b \end{pmatrix}\)
dimana
\(x' = (x-a) \cos \theta - (y-b) \sin \theta + a
\\y' = (x-a) \sin \theta + (y-b) \cos \theta + b
\)
\(= \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & cos\theta \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}\)
dimana
\(x'= x\cos \theta - y \sin \theta \\y' = x \sin \theta + y \cos \theta\)
\(= \begin{pmatrix} \cos\theta & \sin\theta \\ \sin\theta & -cos\theta \end{pmatrix} \begin{pmatrix} x \\ y-c \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}\)
dimana
\(x' = x \cos 2 \theta + (y-c) \sin 2\theta \\
y' = x \sin 2\theta - (y-c) \cos 2\theta + c\)
\(= \begin{pmatrix} \cos \theta & \sin\theta \\ \sin\theta & -cos\theta \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}\)
dimana
\(x'=x \cos 2\theta + y sin 2\theta \\ y'= x \sin 2\theta - y \cos 2\theta\)