from math import cos, sin, pi

class Vector:
  def __init__ (self, x, y):
    self.x = x
    self.y = y

  def translate (self, other):
    if isinstance (other, list):                                                                                                                                                                                   
      return list(map(lambda v: self.translate(v), other))
    if isinstance (other, Vector):
      return Vector(self.x + other.x, self.y + other.y)

  def __str__ (self):
    return "[ {}; {} ]".format(self.x, self.y)

  def __repr__ (self):
    return self.__str__()

class Matrix:
  
  @classmethod
  def rotation (cls, theta):
    return cls(cos(theta), -sin(theta), sin(theta), cos(theta))

  @classmethod
  def scale (cls, s):
    return cls(s, 0, 0, s)

  def __init__ (self, a, b, c, d):
    self.a = a
    self.b = b
    self.c = c
    self.d = d

  def __str__ (self):
    return "[ {} {}; {} {} ]".format(self.a, self.b, self.c, self.d)

  def __repr__ (self):
    return self.__str__()

  def multiply (self, other):
    if isinstance(other, Matrix):
      return Matrix(self.a * other.a + self.b * other.c, 
                    self.a * other.b + self.b * other.d,
                    self.c * other.a + self.d * other.c,
                    self.c * other.b + self.d * other.d)
    if isinstance (other, float):
      return Matrix(other * self.a, other * self.b, other * self.c, other * self.d)
    if isinstance (other, Vector):
      return Vector(self.a * other.x + self.b * other.y, self.c * other.x + self.d * other.y)
    if isinstance (other, list):
      return list(map(lambda v: self.multiply(v), other))