Substituição Ortogonal, Ângulo [;\theta;]

• Mudança de Coordenadas Ortonormal:

  [; \begin{pmatrix}x'\\y'\end{pmatrix} = \underline{\underline{R}}_{\theta} \begin{pmatrix}x\\y\end{pmatrix} = \begin{pmatrix} \cos{\theta} & -\sin{\theta}\\ \sin{\theta} & \cos{\theta} \end{pmatrix} \begin{pmatrix}x\\y\end{pmatrix} \quad \Leftrightarrow \quad ;]

  [; \begin{pmatrix}x\\y\end{pmatrix} = \underline{\underline{R}}_{\theta}^T \begin{pmatrix}x'\\y'\end{pmatrix} = \begin{pmatrix} \cos{\theta} & \sin{\theta}\\ -\sin{\theta} & \cos{\theta} \end{pmatrix} \begin{pmatrix}x'\\y'\end{pmatrix} ;]