How can I uniformly randomly rotate a Vector2 between 0 and 360 degrees?

I have a Vector2:

Vector2 v = new Vector2(1,0开发者_StackOverflow中文版);

How can I randomly rotate this vector (about (0,0)), with a uniform distribution in the range [0,360) degrees?

To randomly rotate a vector v, counter clockwise:

Vector2 v = new Vector2( 1,0 );

Random rnd = new Random();
double rotationAngle = 2.0 * Math.PI * rnd.nextDouble();

Vector2 vRotated = new Vector2( 
   (v.x)*Math.cos(rotationAngle) + (v.y)*Math.sin(rotationAngle),
   (v.y)*Math.cos(rotationAngle) - (v.x)*Math.sin(rotationAngle)
);

The transformation mathematics comes from here