# 2D Transformations are regularly used in Linear Algebra.

# I have added the codes for reflection, projection, scaling and rotation matrices.

import numpy as np


def scaling(scaling_factor):
    return scaling_factor * (np.identity(2))  # This returns a scaling matrix


def rotation(angle):
    arr = np.empty([2, 2])
    c = np.cos(angle)
    s = np.sin(angle)
    arr[0][0] = c
    arr[0][1] = -s
    arr[1][0] = s
    arr[1][1] = c

    return arr  # This returns a rotation matrix


def projection(angle):
    arr = np.empty([2, 2])
    c = np.cos(angle)
    s = np.sin(angle)
    arr[0][0] = c * c
    arr[0][1] = c * s
    arr[1][0] = c * s
    arr[1][1] = s * s

    return arr  # This returns a rotation matrix


def reflection(angle):
    arr = np.empty([2, 2])
    c = np.cos(angle)
    s = np.sin(angle)
    arr[0][0] = (2 * c) - 1
    arr[0][1] = 2 * s * c
    arr[1][0] = 2 * s * c
    arr[1][1] = (2 * s) - 1

    return arr  # This returns a reflection matrix