AABB

/// <summary>
/// Calculates an axis aligned rectangle which fully contains an arbitrarily
/// transformed axis aligned rectangle.
/// </summary>
/// <param name="rectangle">Original bounding rectangle.</param>
/// <param name="transform">World transform of the rectangle.</param>
/// <returns>A new rectangle which contains the trasnformed rectangle.</returns>
public static Rectangle CalculateBoundingRectangle(Rectangle rectangle, Matrix transform)
{
    // Get all four corners in local space
    Vector2 leftTop = new Vector2(rectangle.Left, rectangle.Top);
    Vector2 rightTop = new Vector2(rectangle.Right, rectangle.Top);
    Vector2 leftBottom = new Vector2(rectangle.Left, rectangle.Bottom);
    Vector2 rightBottom = new Vector2(rectangle.Right, rectangle.Bottom);

    // Transform all four corners into work space
    Vector2.Transform(ref leftTop, ref transform, out leftTop);
    Vector2.Transform(ref rightTop, ref transform, out rightTop);
    Vector2.Transform(ref leftBottom, ref transform, out leftBottom);
    Vector2.Transform(ref rightBottom, ref transform, out rightBottom);

    // Find the minimum and maximum extents of the rectangle in world space
    Vector2 min = Vector2.Min(Vector2.Min(leftTop, rightTop),
                              Vector2.Min(leftBottom, rightBottom));
    Vector2 max = Vector2.Max(Vector2.Max(leftTop, rightTop),
                              Vector2.Max(leftBottom, rightBottom));

    // Return as a rectangle
    return new Rectangle((int)min.X, (int)min.Y,
                         (int)(max.X - min.X), (int)(max.Y - min.Y));
}