# rotate ($x, $y, $angle_in_radians) => ($new_x, $new_y)
sub rotate {
    my ($x, $y, $angle) = @_;
    
    my $len = sqrt($x*$x + $y*$y);
    
    $angle += atan2($y, $x);
    
    return
        $len * cos($angle),
        $len * sin($angle);
}