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:
85sq. cm
Step-by-step explanation:
The figure can be divide into 2 rectangles
Area of a rectangle = length * width
For the first rectangle
Area = 9cm * 5cm
Area = 45cm^2
For the second rectangle
Area = 10cm * 4cm
Area = 40cm^2
Area of the figure - 45 + 40
Area of the figure = 85sq. cm
You know 100 cm is one meter. So you multiply 3.9 by 100 = 390
Plz mark mine the brainliest answer:) hope this helped
The volume of cylinder formula is πr²h.
V = π(12)²(9)
V = 1296π³
So the correct answer is 1296π³
Answer:
![(\frac{13}{5};\frac{6}{5}).](https://tex.z-dn.net/?f=%28%5Cfrac%7B13%7D%7B5%7D%3B%5Cfrac%7B6%7D%7B5%7D%29.)
Step-by-step explanation:
![1)\left \{ {{5x=13} \atop {y=2x-4}} \right. \ 2)\left \{ {{x=\frac{13}{5} } \atop {y=\frac{6}{5} }} \right.](https://tex.z-dn.net/?f=1%29%5Cleft%20%5C%7B%20%7B%7B5x%3D13%7D%20%5Catop%20%7By%3D2x-4%7D%7D%20%5Cright.%20%20%5C%202%29%5Cleft%20%5C%7B%20%7B%7Bx%3D%5Cfrac%7B13%7D%7B5%7D%20%7D%20%5Catop%20%7By%3D%5Cfrac%7B6%7D%7B5%7D%20%7D%7D%20%5Cright.)
short explanation: 1) to add the 1st equation to the 2d; 2) to calculate the value of 'x', then to substitute x=13/5 into the 2d equation and calculate the value of 'y'.