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Data Visualizationhard
0:00.0

In a 3D visualization using a coordinate system, a data point PPP is represented by coordinates (x,y,z)(x, y, z)(x,y,z). If a linear transformation matrix T=(1000cos⁡(θ)−sin⁡(θ)0sin⁡(θ)cos⁡(θ))T = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos(\theta) & -\sin(\theta) \\ 0 & \sin(\theta) & \cos(\theta) \end{pmatrix}T=​100​0cos(θ)sin(θ)​0−sin(θ)cos(θ)​​ is applied for rotation, what is the new z′z'z′ coordinate of a point (0,1,1)(0, 1, 1)(0,1,1) with θ=π3\theta = \frac{\pi}{3}θ=3π​?