True or false: The angle formed by rotating a ray about its end point in anticlockwise direction is positive.

Angle of a line with the positive direction of the x-axis is theta . The line is rotated about some point on it in anticlockwise direction by angle 45^0 and its slope becomes 3. Find the angle theta

The point (4,1) undergoes the following three transformations successively (a) Reflection about the line y=x (b)Translation through a distance 2 units along the positive direction of the x-axis ( c) Rotation through an angle pi//4 about the origin in the anti clockwise direction. The final position of the point is given by the co-ordinates

The amount of angle produced by 2 complete recolution of a its end - points as the centre anti - clockwse is 720^@

If the lines represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are rotated about the point (sqrt(3),0) through an angle of 15^0 , one in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

The axes are rotated through an angle pi//3 in the anticlockwise direction with respect to (0,0) . Find the coordinates of point (4,2) (w.r.t. old coordinate system) in the new coordinates system.

The line P Q whose equation is x-y=2 cuts the x-axis at P ,a n dQ is (4,2). The line P Q is rotated about P through 45^0 in the anticlockwise direction. The equation of the line P Q in the new position is

The axes of coordinates are rotated about the z-axis through an angle of pi//4 in the anticlockwise direction and the components of a vector are 2sqrt2, 3sqrt2, 4 . Prove that the components of the same vector in the original system are -1, 5, 4 .

If the lines represented by x^2-2pxy-y^2=0 are rotated about the origin through an angle theta , one clockwise direction and other in anti-clockwise direction, then the equation of the bisectors of the angle between the lines in the new position is