!$ { \begin{bmatrix} dd\\d \theta \end{bmatrix}} = { \begin{bmatrix} 1\,\,{ \large sin \theta \over cos \theta} \\ { \large 1 \over L.cos \theta} \end{bmatrix}}. { \begin{bmatrix} dx\\dy \end{bmatrix}} !$

!$ { \begin{bmatrix} dd\\d \theta \end{bmatrix}} = { \begin{bmatrix} 1\,\,-L.sin \theta\\0\,\,\,\,\,\,\,L.cos \theta \end{bmatrix}}. { \begin{bmatrix} dx\\dy \end{bmatrix}} !$

!$ { \begin{bmatrix} dd\\d \theta \end{bmatrix}} ={ \begin{bmatrix} L.cos \theta\,\,0\\L.sin \theta\,\,1 \end{bmatrix}}. { \begin{bmatrix} dx\\dy \end{bmatrix}} !$

!$ { \begin{bmatrix} dd\\d \theta \end{bmatrix}} = { \begin{bmatrix} L.cos \theta\,\,L.sin \theta\\\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1 \end{bmatrix}}. { \begin{bmatrix} dx\\dy \end{bmatrix}} !$

!$ { \begin{bmatrix} dd\\d \theta \end{bmatrix}} = { \begin{bmatrix} 1\,\,\,\,\,\,\,\,\,\,0\\{ \large sin \theta \over cos \theta}\,\,{ \large 1 \over L.cos \theta} \end{bmatrix}}. { \begin{bmatrix} dx\\dy \end{bmatrix}} !$