I was reading a book in which it is mentioned that: Rotate coordinate axes by $45$ degrees so that a point $(x,y)$ becomes $(x+y,y-x)$ . Here is image 1 H...

I do not know if it is the right section to ask for it, but I wanted to ask some questions about math symbols that I often find on automation books. One o...

The John Deere Company has found that the revenue from sales of heavy-duty tractors is a function of the unit price p that it charges. If the revenue $R$ ...

Determine which of the following transformations are linear transformations A. The transformation $T_1$ defined by $T_1(x_1,x_2,x_3)=(x_1,0,x_3)$ B. The t...

Prove that the Laplacian matrix $L$ of a graph $G$ satisfies the following: For every vector $v \in \mathbf{R}^n$ we have $$v^TLv=\frac{1}{2}\sum_{i,j=1}^...

I only knew this angle symbol "$\angle$", which is usually used to represent acute angles. But now I have accounted a problem, where I wanted to represent...

There are 20 students in the high school glee club. They need to pick four students to serve as the student representatives for an upcoming trip. How many...

Is it possible to find the coordinates of the point marked (?,?) if I have a rectangle/right triangle with a given point and the length of the hypotenuse?...

Let $X$ a set not empty and $(X,d)$ a metric space. Prove he union of two open sets is open. My proof: Let $A_1,A_2$ open sets, we need to prove $A_1\cup ...

Quadratic equation, $ax^2+bx+c=0$ and its solution is quadratic equation, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ Now setting $a=1$ then we have $x^2+bx+c=0$ ...