Mat4 RotationMatrix(float radians)
{
    Mat4 result;

    // assuming column-major order (first index is column, second is row)
    result[0][0] = Math.Cos(radians);
    result[0][1] = -Math.Sin(radians);
    result[1][0] = Math.Sin(radians);
    result[1][1] = Math.Cos(radians);

    return result;
}

Mat4 MirrorXMatrix()
{
    Mat4 result;

    result[0][0] = -1.0f;
    result[0][1] = 0.0f;
    result[1][0] = 0.0f;
    result[1][1] = 1.0f;

    return result;
}

Mat4 ScaleMatrix(float x, float y)
{
    Mat4 result;

    result[0][0] = x;
    result[0][1] = 0;
    result[1][0] = 0;
    result[1][1] = y;

    return result;
}

int main()
{
    float heading = 0.2f;
    float scaleX = 2.0f;
    float scaleY = 3.0f;

    // because the order of transformations goes right to left, this matrix will rotate, then mirror, then scale.
    Mat4 shipMatrix = ScaleMatrix(scaleX, scaleY) * MirrorXMatrix() * RotateMatrix(heading);

    // assume we have ship.Points or whatever
    for (int i = 0; i < ship.Points.Length; i++)
    {
        Vec2 transformedPoint = shipMatrix * ship.Points[i];
        // now do whatever with it
    }
}