$$ \begin{pmatrix} 1 & 0 & 0 & t_x \\ 0 & 1 & 0 & t_y \\ 0 & 0 & 1 & t_z \\ 0 & 0 & 0 & 1 \\ \end{pmatrix} \begin{pmatrix} x \\ y \\ z \\ 1 \\ \end{pmatrix} = \begin{pmatrix} x + t_x \\ y + t_y \\ z + t_z \\ 1 \\ \end{pmatrix} $$
$$ \begin{pmatrix} s_x & 0 & 0 & 0 \\ 0 & s_y & 0 & 0 \\ 0 & 0 & s_z & 0 \\ 0 & 0 & 0 & 1 \\ \end{pmatrix} \begin{pmatrix} x \\ y \\ z \\ 1 \\ \end{pmatrix} = \begin{pmatrix} x * s_x \\ y * s_y \\ z * s_z \\ 1 \\ \end{pmatrix} $$
$$ \begin{pmatrix} cos\theta & -sin\theta & 0 \\ sin\theta & cos\theta & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} \begin{pmatrix} x \\ y \\ 1 \\ \end{pmatrix} = \begin{pmatrix} xcos\theta - ysin\theta \\ xsin\theta + ycos\theta \\ 1 \\ \end{pmatrix} $$
$$ \begin{pmatrix} cos\theta & -sin\theta & 0 & 0 \\ sin\theta & cos\theta & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{pmatrix} \begin{pmatrix} x \\ y \\ z \\ 1 \\ \end{pmatrix} = \begin{pmatrix} xcos\theta - ysin\theta \\ xsin\theta + ycos\theta \\ z \\ 1 \\ \end {pmatrix} $$
$$ \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & cos\theta & -sin\theta & 0 \\ 0 & sin\theta & cos\theta & 0 \\ 0 & 0 & 0 & 1 \\ \end{pmatrix} \begin{pmatrix} x \\ y \\ z \\ 1 \\ \end{pmatrix} = \begin{pmatrix} x \\ ycos\theta - zsin\theta \\ ysin\theta + zcos\theta \\ 1 \\ \end {pmatrix} $$
$$ \begin{pmatrix} cos\theta & 0 & sin\theta & 0 \\ 0 & 1 & 0 & 0 \\ -sin\theta 0 & cos\theta & 0 \\ 0 & 0 & 0 & 1 \\ \end{pmatrix} \begin{pmatrix} x \\ y \\ z \\ 1 \\ \end{pmatrix} = \begin{pmatrix} xcos\theta + zsin\theta \\ y \\ -xsin\theta + zcos\theta \\ 1 \\ \end {pmatrix} $$