Given the following matrices, what is AB?

$$Compute\lim_{x\rightarrow0\ }\ \frac{\sin\ \left(1-\sqrt[]{x}\right)}{x-1}$$

In how many ways can you rearrange the letters of “HMMTHMMT" such that the consecutive substring “HMMT" does not appear?

Let $$f:\ R→R$$ be a function such that $$f(a+b)=f(a)+f(b)$$ and that $$f(2022)=3033$$ .  What is $$f(2023)$$ ?

Square 

OPQR has vertices $$O(0,0),\ P(0,8),\ Q(8,8)\ and\ R(8,0)$$ . The parabola with equation $$y=a(x-2)(x-6)$$ intersects the side OR at points K and L, the side OP at point N and the side RQ at point M, as shown. If the area of trapezoid formed by joining K,L,M and N is 36, what is the value of a? 

Draw a conclusion from the statements.

If a whole number is even, then its square is divisible by 4.

The number I am thinking of is an even number.

What is the exact value of cos 3.75°?

Mrs. Terrobias bought a brand new king-sized bed for Php 35,000.00 through her credit card. After 3 months, she found out that she was charged with an additional Php 3,000.00. How much was the monthly interest rate applied to Mrs. Terrobias’ credit card?