D.16 because the coefficient is a number placed before the veritable it’s being multiples by
Answer:
Option B is correct.
Rotation matrix = ![\begin{bmatrix} -3.96 \\ -1.13 \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%20-3.96%20%5C%5C%20-1.13%20%5Cend%7Bbmatrix%7D)
Step-by-step explanation:
Given a vector :
, rotation by
radian.
A rotation matrix is a matrix that is used to perform a rotation in Euclidean space.
The standard rotation matrix is given by;
R = ![\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%5Ccos%20%5Ctheta%20%26%20-%5Csin%20%5Ctheta%20%5C%5C%20%5Csin%20%5Ctheta%20%26%20%5Ccos%20%5Ctheta%20%5Cend%7Bbmatrix%7D)
Then, the matrix of rotation by
radian is:
=
![\begin{bmatrix}x \\ y\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Dx%20%5C%5C%20y%5Cend%7Bbmatrix%7D)
Then; substitute ![\theta = 120^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20120%5E%7B%5Ccirc%7D)
![\begin{bmatrix}x' \\ y'\end{bmatrix}= \begin{bmatrix}\cos 120^{\circ} & -\sin 120^{\circ} \\ \sin 120^{\circ} & \cos 120^{\circ}\end{bmatrix}\begin{bmatrix}1 \\ 4 \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Dx%27%20%5C%5C%20y%27%5Cend%7Bbmatrix%7D%3D%20%5Cbegin%7Bbmatrix%7D%5Ccos%20120%5E%7B%5Ccirc%7D%20%26%20-%5Csin%20120%5E%7B%5Ccirc%7D%20%5C%5C%20%5Csin%20120%5E%7B%5Ccirc%7D%20%26%20%5Ccos%20120%5E%7B%5Ccirc%7D%5Cend%7Bbmatrix%7D%5Cbegin%7Bbmatrix%7D1%20%5C%5C%204%20%5Cend%7Bbmatrix%7D)
or
![\begin{bmatrix}x' \\ y'\end{bmatrix}= \begin{bmatrix} -0.5 & -0.866 \\ 0.866 & -0.5 \end{bmatrix}\begin{bmatrix}1 \\ 4 \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Dx%27%20%5C%5C%20y%27%5Cend%7Bbmatrix%7D%3D%20%5Cbegin%7Bbmatrix%7D%20-0.5%20%26%20-0.866%20%5C%5C%200.866%20%26%20-0.5%20%5Cend%7Bbmatrix%7D%5Cbegin%7Bbmatrix%7D1%20%5C%5C%204%20%5Cend%7Bbmatrix%7D)
or
![\begin{bmatrix}x' \\ y'\end{bmatrix}= \begin{bmatrix} -0.5 +4(-0.866) \\ 0.866+4(-0.5)\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Dx%27%20%5C%5C%20y%27%5Cend%7Bbmatrix%7D%3D%20%5Cbegin%7Bbmatrix%7D%20-0.5%20%2B4%28-0.866%29%20%5C%5C%200.866%2B4%28-0.5%29%5Cend%7Bbmatrix%7D)
Simplify:
![\begin{bmatrix}x' \\ y'\end{bmatrix} = \begin{bmatrix} -3.96 \\ -1.13 \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Dx%27%20%5C%5C%20y%27%5Cend%7Bbmatrix%7D%20%3D%20%5Cbegin%7Bbmatrix%7D%20-3.96%20%5C%5C%20-1.13%20%5Cend%7Bbmatrix%7D)
Therefore, the rotation matrix of a given vector is, ![\begin{bmatrix} -3.96 \\ -1.13 \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%20-3.96%20%5C%5C%20-1.13%20%5Cend%7Bbmatrix%7D)
Answer:
If KE = OS then we can deduce that the trapezoid is constructed of 3 equilateral triangles and thus we can easily work out the angles.
OSK = 60
SKE = 120
KEP = 120
EPO = 60
We can also easily work out the perimeter since we can deduce that PE = SK = KE and thus the perimeter is 5 * 8 = 40
Answer:
21
Step-by-step explanation:
This is a substitution question,we are to substitute a given value in place of a certain letter
So let's solve
2x^2-x
And since x is given to be -3
So let's substitute
2(-3)^2-(-3)
2(9)-(-3)
18+3
21
So the final answer is 21
3x15=45 and 17x15=255 so 45+255=300