Calculate the rotation of the vector

Question

Calculate the rotation of the vector

[-2

-9]  by 90 degrees about the origin (take positive angles to be anticlockwise).

Enter answer exactly using appropriate trigonometric expressions if required.

Resultant vector: [           ]

               [           ]

Answer 1

given vector is in quadrant 3 with magnitude = sqr(4+81) = sqr86

and with reference angle = exactly arctan(9/2) = about 77.6 degrees

and actual angle = exactly 180+arctan4.5 = about 257.6

after a 90 degrees counterclockwise rotation the new vector is exactly [9 2], just change both signs and switch the x and y components