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poizon [28]
3 years ago
10

What degree of rotation is represented on this matrix

Mathematics
1 answer:
Korvikt [17]3 years ago
7 0

Answer:

Option B is correct

the degree of rotation is, -90^{\circ}

Step-by-step explanation:

A rotation matrix is a matrix that is used to perform a rotation in Euclidean space.

To find the degree of rotation using a standard rotation matrix i.e,

R = \begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}

Given the matrix: \begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}

Now, equate the given matrix with standard matrix we have;

\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} =  \begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}

On comparing we get;

\cos \theta = 0       and -\sin \theta =1  

As,we know:

  • \cos \theta = \cos(-\theta)
  • \sin(-\theta) = -\sin \theta

\cos \theta = \cos(90^{\circ}) = \cos( -90^{\circ})

we get;

\theta = -90^{\circ}

and

\sin \theta =- \sin (90^{\circ}) = \sin ( -90^{\circ})

we get;

\theta = -90^{\circ}

Therefore, the degree of rotation is, -90^{\circ}

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All other things being equal, the motorist should cover more than 250 miles with 16 gallons of gas.

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x =  \frac{4000}{11}   = 363.6 \: miles


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Step-by-step explanation:

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2 years ago
Joy is making a fruit salad. For every 2 cups of blueberries that Joy uses in the fruit salad, she uses 3 cups of strawberries.
Igoryamba

Joy will need to use 9 cups of strawberries for 6 cups of blueberries.

Step-by-step explanation:

Given,

Cups of blueberries used for 3 cups of strawberry = 2

Ratio of cups of blueberry to strawberry = 2:3

Joy wants to use 6 cups of blueberries.

Let,

x be the cups of strawberry for 6 cups of blueberries.

Ratio of cups of blueberries to strawberries = 6:x

Using proportion;

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Product of extreme = Product of mean

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Dividing both sides by 2

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Joy will need to use 9 cups of strawberries for 6 cups of blueberries.

Keywords: ratio, proportion, division

Learn more about division at:

  • brainly.com/question/10480770
  • brainly.com/question/10546617

#LearnwithBrainly

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