Matrices are commonly used to encrypt data. here is a simple form such an encryption can take. first, we represent each letter in the alphabet by a number, so let us take < space > = 0, a = 1, b = 2, and so on. thus, for example, "abort mission" becomes [1 2 15 18 20 0 13 9 19 19 9 15 14]. to encrypt this coded phrase, we use an invertible matrix of any size with integer entries. for instance, let us take a to be the 2 × 2 matrix 4 3 1 2 . we can first arrange the coded sequence of numbers in the form of a matrix with two rows (using zero in the last place if we have an odd number of characters) and then multiply on the left by a. encrypted matrix = 4 3 1 2 1 15 20 13 19 9 14 2 18 0 9 19 15 0 = 10 114 80 79 133 81 56 5 51 20 31 57 39 14 , which we can also write as [10 5 114 51 80 20 79 31 133 57 81 39 56 14]. to decipher the coded message, multiply the encrypted matrix by a−1. the following question uses the above matrix a for encoding and decoding. decode the following message, which was encrypted using the matrix a. (include any appropriate spaces in your answer.) [57 33 126 54 29 11 80 20 46 29 145 65 74 41]

We as humans write math expression in infix notation, e.g. 5 + 2 (the operators are written in-between the operands). in a computer’s language, however, it is preferred to have the operators on the right side of the operands, i.e. 5 2 +. for more complex expressions that include parenthesis and multiple operators, a compiler has to convert the expression into postfix first and then evaluate the resulting postfix.write a program that takes an “infix” expression as input, uses stacks to convert it into postfix expression, and finally evaluates it. it must support the following operations: + - / * ^ % (example infix expression: (7 - 3) / (2 + 2)postfix expression: 7 3 - 2 2 + /result: 1guidelines: 1. you will need to use stacks in three placesa. one for the parenthesis check [char stack]b. one during infix to postfix [char stack]c. one during evaluation [int stack]for a and b above, you can use same array and same push, pop method as both ofthem are char. but for evaluation you have int stack and you might consider to createanother push pop method to handle it. maybe push_int, pop_int, etc. or find otherstrategy to utilize existing push pop method2. you can create a function for obtaining operator priority. that function should take anoperator as input and return its priority as an integer. this function will you a lot andreduce repeated code3. during evaluation you will need to convert char into integer. example for single digit: char c = '5'; int x = c - '0';

When creating a budget, log fixed expenses before income. after income. after savings. at the top.

Select the correct answer. sean is a computer programmer. he has programmed an application for toddlers that plays nursery rhymes. however, a logic error has occurred in the program. which problem is a likely consequence of the error? a. the program crashes every time the user wants to play the nursery rhymes. b. the program crosses its buffer boundaries and overwrites an adjacent program. c. the program plays a different nursery rhyme than the one the user intended to play. d. the program shows different structures in its programming language code. e. the program introduces new viruses every time the user plays a nursery rhyme.