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vivado [14]
2 years ago
14

Find the matrix for the linear transformation which rotates every vector in r2 through an angle of −π/3.

Mathematics
1 answer:
enot [183]2 years ago
5 0

The matrix for the linear transformation for which rotates every vector in r2 is \left[\begin{array}{cc}\frac{1}{2}  &\frac{\sqrt{3} }{2}  \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right].

In this question,

The angle is -π/3 = -60°

Clockwise rotations are denoted by negative numbers.

Matrix for counter-clockwise direction for an angle α is

\left[\begin{array}{cc}cos\alpha &-sin\alpha \\-sin\alpha &cos\alpha \end{array}\right]

Then, matrix for clockwise direction for an angle α

Put α = -α in the above matrix,

⇒ \left[\begin{array}{cc}cos(-\alpha) &-sin(-\alpha) \\-sin(-\alpha) &cos(-\alpha) \end{array}\right]

⇒ \left[\begin{array}{cc}cos\alpha &sin\alpha \\sin\alpha &cos\alpha \end{array}\right]

Now substitute α = 60°

Then matrix becomes,

⇒ \left[\begin{array}{cc}cos60 &sin60 \\sin60 &cos60 \end{array}\right]

⇒ \left[\begin{array}{cc}\frac{1}{2}  &\frac{\sqrt{3} }{2}  \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right]

Hence we can conclude that the matrix for the linear transformation for which rotates every vector in r2 is \left[\begin{array}{cc}\frac{1}{2}  &\frac{\sqrt{3} }{2}  \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right].

Learn more about matrix for linear transformation here

brainly.com/question/12486975

#SPJ4

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garri49 [273]

\\ \sf\longmapsto \dfrac{1-cos2A}{1-sin2A}

<h3>LHS</h3>

\boxed{\sf \dfrac{cosA}{sinA}=cotA}

\\ \sf\longmapsto \dfrac{1-cos2A}{1-sin2A}

\\ \sf\longmapsto 1-cot2A

\\ \sf\longmapsto 1-\dfrac{1}{tan2A}

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\\ \sf\longmapsto tan2A

8 0
3 years ago
Who ever answers this first gets brainly
Alex777 [14]

Answer: A

im sure

Step-by-step explanation:

7 0
3 years ago
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I hate math bro please help me ill mark u brainliest
yulyashka [42]
Please mark me brainless :)
5 0
3 years ago
If 140 people were surveyed, how many preferred crab?
Cloud [144]

If 140 people were surveyed, from the given table, the number of people that preferred crab is; 42

<h3>How to work with percentages?</h3>

We are given;

Total sample size; n = 140

Now, from the table we see the percentages that preffered each seafood.

Percentage that preferred Shrimp = 24%

Percentage that preferred Crab = 30%

Percentage that preferred Fish = 36%

Percentage that preferred Neither = 10%

Thus;

Number that preferred Crab = 30% * 140

Number that preferred Crab = 42 people

Read more about Percentages at; brainly.com/question/843074

5 0
2 years ago
Does anyone have an answer to this question?
grigory [225]

Answer:

8.9 cm to 1 dec. place.

Step-by-step explanation:

First, use Pythagoras to find the length of BD.

BD^2 = 6^2 + 7^2 = 85

BD = √85.

BM = √85 / 2.

Consider the triangle TBM, by Pythagoras:

TB^2 = BM^2 + MT^2

MT^2 = 10^2 - (√85 / 2  )^2

= 100 - 21.25

= 78.75.

MT = 8.874

5 0
2 years ago
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