Which matrix represents the rotation of the vector 1,4 by 2pi/3 radians

Option B is correct.

Rotation matrix =

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 =

Then, the matrix of rotation by radian  is:

=

Then; substitute

or

or

Simplify:

Therefore, the rotation matrix of a given vector is,

answer: i believe c. is the answer sorry if i am wrong

step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it