Mathematics, 03.02.2020 02:01 lizzyhearts
Find the matrix a of the linear transformation t from ℝ2 to ℝ2 that rotates any vector through an angle of 150∘ in the clockwise direction.
Answers: 3
![A=\left[\begin{array}{cc}-\frac{\sqrt{3} }{2} &\frac{1}{2} \\-\frac{1}{2} &-\frac{\sqrt{3} }{2}\end{array}\right]](/tpl/images/0494/8116/79a5f.png)
, can be described with the help of trigonometric functions.![\left[\begin{array}{cc}\cos \theta&-\sin \theta\\\sin \theta&\cos \theta\end{array}\right]](/tpl/images/0494/8116/bd6f0.png)
describes the counterclockwise rotation of the 
plane by an angle of 
to obtain:![\left[\begin{array}{cc}\cos (-\theta)&-\sin (-\theta)\\\sin (-\theta)&\cos (-\theta)\end{array}\right]](/tpl/images/0494/8116/e0c9f.png)
![\left[\begin{array}{cc}\cos (\theta)&\sin (\theta)\\-\sin (\theta)&\cos (\theta)\end{array}\right]](/tpl/images/0494/8116/ac9b1.png)
.
clockwise is:![\left[\begin{array}{cc}\cos (150\degree)&\sin (150\degree)\\-\sin (150\degree)&\cos (150\degree)\end{array}\right]=\left[\begin{array}{cc}-\frac{\sqrt{3} }{2} &\frac{1}{2} \\-\frac{1}{2} &-\frac{\sqrt{3} }{2}\end{array}\right]](/tpl/images/0494/8116/512f5.png)
.
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Find the matrix a of the linear transformation t from ℝ2 to ℝ2 that rotates any vector through an an...
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