import math
import numpy as np

def translate(x, y, z):
    return np.array([
        [1, 0, 0, 0],
        [0, 1, 0, 0],
        [0, 0, 1, 0],
        [x, y, z, 1]
    ])

def rotate_x(a):
    return np.array([
        [1, 0, 0, 0],
        [0, math.cos(a), math.sin(a), 0],
        [0, -math.sin(a), math.cos(a), 0],
        [0, 0, 0, 1]
    ])

def rotate_y(a):
    return np.array([
        [math.cos(a), 0, -math.sin(a), 0],
        [0, 1, 0, 0],
        [math.sin(a), 0, math.cos(a), 0],
        [0, 0, 0, 1]
    ])

def rotate_z(a):
    return np.array([
        [math.cos(a), math.sin(a), 0, 0],
        [-math.sin(a), math.cos(a), 0, 0],
        [0, 0, 1, 0],
        [0, 0, 0, 1]
    ])

def scale(n):
    return np.array([
        [n, 0, 0, 0],
        [0, n, 0, 0],
        [0, 0, n, 0],
        [0, 0, 0, 1]
    ])