implement in python.

Use Python.   Q1. Suppose deg is an angle in degrees.  Write down the NumPy code that computes the counterclockwise rotation matrix.  Don't forget to convert the angles into radians when necessary.   def rotate(deg):   Q2. Let x be a vector.  How do you use rotate(deg) to find a vector y that is normal to x?  Namely <x,y> = 0.   y = ...   Q3. Let x be a vector.  How do you find a vector v in the same direction as x but with |v| = 1.   v = ...   Q4. A hyperplane in 2D is the same as a line.  A hyperplane is defined by a normal vector w and a bias scalar b.  Write down the expression that defines points on the line that is the hyperplane in 2D defined by (w, b).   { x : ... }   Q5. Given a vector x, and a hyperplane P defined by (w, b).  Describe how to compute the point v that is the projection of x on to the plane P.

You will be given a list of tuples where each tuple indicates a point i.e. (x, y) in a 2-dimensional coordinate system. You need to write a python program to find the minimum distance and the point that is closest to the origin i.e. (0,0) ===================================================== Hint: The formula of distance = √((Δx)2+(Δy)2) As you are calculating the distance from the origin (0,0), you can simply usedistance = √(x2+y2) You can create a list of distances from each point and sort that list using your personal favorite sorting algorithm. You can use python build-in functions for list: list.index(), min() ===================================================== Sample Input 1 [(5,3), (2,9), (-2,7), (-3,-4), (0,6), (7,-2)] Sample Output 1 The closest point is (-3, -4) which has a distance of 5.0 from the origin. ===================================================== Sample Input 1 [(1,7), (4,5), (-1,7), (-2,0), (1,1), (5,-1)] Sample Output 1 The closest point is (1, 1) which has a…

Write a program that finds the factorials of integers from 1 to 5. Write the results in the form of a table. Do the programming in C language. Thanks.