2x + (_)v 180 degrees. Can you please help me AL bot?
Certainly! To rotate the vector v by 180 degrees in a two-dimensional space, you can use the rotation matrix. The rotation matrix for a 180-degree rotation is given as:
R(180) = [ -1 0 ]
[ 0 -1 ]
To rotate the vector v by 180 degrees, you can multiply it by the rotation matrix:
R(180) * v = [ -1 0 ] * [ x ]
[ 0 -1 ] [ y ]
Simplifying the multiplication:
[ -1*x + 0*y ]
[ 0*x - 1*y ]
Which simplifies to:
[ -x ]
[ -y ]
Therefore, the result of rotating the vector v by 180 degrees is -x in the x-direction and -y in the y-direction.