





from __future__ import annotations

from typing import Any







class 		_lowerCAmelCase:

  """simple docstring"""







  def __init__(   self    ,							UpperCAmelCase    ,							UpperCAmelCase      )->   None:  # noqa: A002
     __A    =  item
     __A    =  next







class 		_lowerCAmelCase:

  """simple docstring"""







  def __init__(   self      )->   None:
     __A    =  None
     __A    =  0

  def 						SCREAMING_SNAKE_CASE__			(   self    ,							UpperCAmelCase      )->   None:
     __A    =  Node(__lowerCamelCase    ,							self.head      )
     self.size += 1

  def 						SCREAMING_SNAKE_CASE__			(   self      )->   Any:




     if self.head is None:
        return None
     else:
        __A    =  self.head.item
        __A    =  self.head.next
        self.size -= 1
        return item

  def 						SCREAMING_SNAKE_CASE__			(   self      )->   bool:
     return self.head is None

  def __str__(   self      )->   str:




     if self.is_empty():
        return ""
     else:
        __A    =  self.head
        __A    =  ''''''
        __A    =  []
        while iterate:
           item_list.append(str(iterate.item      )      )
           __A    =  iterate.next

        __A    =  ''' --> '''.join(__lowerCamelCase      )

        return item_str





  def __len__(   self      )->   int:
     return self.size









'''simple docstring'''





from math import cos, sin






def  lowerCamelCase_  (     lowercase__):
 lowerCamelCase__	=  float(lowercase__)
 return [[scaling_factor * int(x == y) for x in range(2)] for y in range(2)]






def  lowerCamelCase_  (     lowercase__):
 lowerCamelCase__	,						lowerCamelCase__	=  cos(lowercase__), sin(lowercase__)
 return [[c, -s], [s, c]]






def  lowerCamelCase_  (     lowercase__):
 lowerCamelCase__	,						lowerCamelCase__	=  cos(lowercase__), sin(lowercase__)
 lowerCamelCase__	=  c * s
 return [[c * c, cs], [cs, s * s]]






def  lowerCamelCase_  (     lowercase__):
 lowerCamelCase__	,						lowerCamelCase__	=  cos(lowercase__), sin(lowercase__)
 lowerCamelCase__	=  c * s
 return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(F"""    {scaling(5) = }""")
print(F"""  {rotation(45) = }""")
print(F"""{projection(45) = }""")
print(F"""{reflection(45) = }""")

