Mathematics, 05.07.2020 16:01 lorraneb31
Make a matrix A whose action is described as follows: The hit by A rotates everything Pi/4 counterclockwise radians, then stretches by a factor of 1.8 along the x-axis and a factor of 0.7 along the y-axis and then rotates the result by Pi/3 clockwise radians.
Answers: 3
![A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right]](/tpl/images/0701/8053/fc178.png)
![P = \left[\begin{array}{ccc}cos\pi/4&-sin\pi/4\\sin\pi/4&cos\pi/4\end{array}\right]](/tpl/images/0701/8053/0bf01.png)
![P = \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right]](/tpl/images/0701/8053/d1119.png)
![\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}cos\theta&-sin\theta\\sin \theta&cos\theta\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]](/tpl/images/0701/8053/32c80.png)
![\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]](/tpl/images/0701/8053/7c528.png)
![Q = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right]](/tpl/images/0701/8053/74430.png)
![R = \left[\begin{array}{ccc}cos(-\pi/3)& -sin(-\pi/3)\\-sin(\pi/3)&cos(\pi/3)\end{array}\right]](/tpl/images/0701/8053/8171f.png)
![R = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right]](/tpl/images/0701/8053/0edeb.png)
![A = RQP = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right] \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right]](/tpl/images/0701/8053/314ab.png)
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Make a matrix A whose action is described as follows: The hit by A rotates everything Pi/4 countercl...
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