Substituição Ortogonal, Ângulo $\theta$

• Mudança de Coordenadas Ortonormal:

  $\left(\begin{array}{c}{x}^{\prime }\\ y^{\prime }\end{array}\right)={\underset{―}{\underset{―}{R}}}_{\theta }\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)\iff$

  $\left(\begin{array}{c}x\\ y\end{array}\right)={\underset{―}{\underset{―}{R}}}_{\theta }^T\left(\begin{array}{c}{x}^{\prime }\\ y^{\prime }\end{array}\right)=\left(\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right)\left(\begin{array}{c}{x}^{\prime }\\ y^{\prime }\end{array}\right)$