If a rotation matrix R=(cosθ−sinθsinθcosθ)R = \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix}R=(cosθsinθ−sinθcosθ) is applied twice, what is the resulting matrix?
(cos(2θ)−sin(2θ)sin(2θ)cos(2θ))\begin{pmatrix} \cos(2\theta) & -\sin(2\theta) \\ \sin(2\theta) & \cos(2\theta) \end{pmatrix}(cos(2θ)sin(2θ)−sin(2θ)cos(2θ))
(cos2θ−sin2θsin2θcos2θ)\begin{pmatrix} \cos^2 \theta & -\sin^2 \theta \\ \sin^2 \theta & \cos^2 \theta \end{pmatrix}(cos2θsin2θ−sin2θcos2θ)
(1001)\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}(1001)
(cos(θ2)−sin(θ2)sin(θ2)cos(θ2))\begin{pmatrix} \cos(\theta^2) & -\sin(\theta^2) \\ \sin(\theta^2) & \cos(\theta^2) \end{pmatrix}(cos(θ2)sin(θ2)−sin(θ2)cos(θ2))