Find the transformation matrix that rotates a rectangular coordinate system through an angle of 60 about axes equal angels with original thr

Question

Find the transformation matrix that rotates a rectangular coordinate system through an angle of 60 about axes equal angels with original three coordinate axes

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Adela 4 years 2021-07-13T15:17:08+00:00 1 Answers 19 views 0

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  1. minhkhue
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    2021-07-13T15:18:10+00:00
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    Answer:

      M = \left[\begin{array}{ccc}cos \ 60&0\\0&-sin \ 60\end{array}\right]

    Explanation:

    To find the matrix, let’s decompose the vectors, the rotated angle is (-60C) for the prime system

              x ’= x cos (-60)

              y ’= y sin (-60)

    we use

              cos 60 = cos (-60)

              sin 60 = – sin (-60)

    we substitute

              x ’= x cos 60

              y ’= – y sin 60

    the transformation system is

             \left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}cos 60&0\\0&-sin60\end{array}\right] \ \left[\begin{array}{ccc}x\\y\end{array}\right]x ‘

    the transformation matrix is

           M = \left[\begin{array}{ccc}cos \ 60&0\\0&-sin \ 60\end{array}\right]

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