### Find x such that the matrix is equal to its own inverse.

] The aim of the article is to find the value of the variable $x$ within the given matrix for which it will be equal to its inverse matrix. The basic

### Find a function f such that f'(x)=3x^3 and the line 81x+y=0 is tangent to the graph of f.

The aim of the question is to find the function whose first derivative is given as well as the equation tangent to it. The basic concept behind this

### Compilers can have a profound impact on the performance of an application. Assume that for a program, compiler A results in a dynamic instruction count of 1.0E9 and has an execution time of 1.1 s, while compiler B results in a dynamic instruction count of 1.2E9 and an execution time of 1.5 s.

Given that the processor’s clock cycle time is 1 ns, calculate each program’s average CPI under this situation. Assume there are two

### Find the maximum and minimum values attained by the function f along the path c(t).

This problem refers to calculus and aims to understand that over a closed and bounded interval, the continuous function of

### What is the probability that the sum of the numbers on two dice is even when they are rolled?

This problem aims to familiarize us with random events and their predictable outcomes. The concepts required to solve this problem are mostly related