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Design a matrix M that is 3x3 and that when multiplied by a vector in R3,...

Design a matrix M that is 3x3 and that when multiplied by a vector in R3, rotates that vector counter-clockwise by 30 degrees around the z-axis. Compute the real and complex eigenvalues of your matirx. Write the complex eigenvalues in the form cosθ+isinθ. What is θ?

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