Exercise 1: Given a DNA string, find all genes it contains.

Background: Biologists use a simple model to represent the building blocks of life, in which the letters A, C, G, and T represent the four bases in the DNA of living organisms. A gene is a substring that represents a functional unit of critical importance in understanding life processes.

A gene has following properties:

• It begins with the start codon ATG.
• Its length is a multiple of 3.
• It ends with one of the stop codons TAG, TAA, or TGA.
• It has no intervening stop codons.

Example: if String DNA = "ATAGATGCATAGCGCATAGCTAGATGTGCTGAC"

Then ATGCATAGCGCATAG and ATGTGCTGA are two genes inside DNA.

Exercise 2:

Write a program Rotation.java that takes two command-line arguments (the name of an image file and a real number r and rotates the image r degrees counterclockwise. To rotate, copy the color of each pixel (si,sj) in the source image to a target pixel (ti,tj) whose coordinates are given by the following formulas:

**ti = (si - ci) cos r - (sj -cj) sin r + ci

**tj = (si - ci) sin r + (sj -cj) cos r + cj

where (ci, cj) is the center of the image.

Exercise 3:

Creating a swirl effect is similar to rotation, except that the angle r changes as a function of distance to the center of the image. Use the same formulas as in the previous exercise, but compute r as a function of (si,sj), specifically Pi/256 times the distance to the center.