Explanation

The orthocenter is the point where the three altitudes of a triangle intersect.

An altitude is a perpendicular line from a vertex to the opposite side (or its extension).

Explanation

Given the product:

(5i) × (-2i)

= -10i²

Since i² = -1:

= -10(-1)

= 10

Explanation

The equation a(b + c) = ab + ac shows how multiplication distributes over addition.

This is called the distributive property in algebra.

Explanation

2x=1⇒x=0(since 20=1)

Explanation

The cube roots of unity are:  

1, ω, and ω², where:

- ω = -1/2 + (√3/2)i  

- ω² = -1/2 - (√3/2)i  

These are the complex cube roots of unity, and they satisfy:

1 + ω + ω² = 0  

and  

1 × ω × ω² = 1

Explanation

If $f(x) = 5$, then what is$f'(x)$ at $x = 1$?

This is a constant function, meaning:

$$f(x) = 5 quad text{for all } x$$

The derivative of a constant is always:

$$f'(x) = 0$$

Explanation

$$lim_{x to a} (2x + 4)$$

Assuming the question meant:

lim​ x→3 ​(2x+4)

Then:

$$lim_{x to 3} (2x + 4) = 2(3) + 4 = 6 + 4 = 10$$x→3 (2x+4)=2(3)+4=6+4=10

Explanation

The transpose of a row matrix is a column matrix.

Similarly, the transpose of a column matrix is a row matrix.

In essence, when transposing a matrix, you swap rows with columns.

So, a matrix with one row becomes a matrix with one column, and vice versa. 

Explanation

The transpose of a row matrix is a column matrix.

Similarly, the transpose of a column matrix is a row matrix.

In essence, when transposing a matrix, you swap rows with columns.

So, a matrix with one row becomes a matrix with one column, and vice versa. 

Explanation

• A Row Matrix has only one row and multiple columns.

  $$[1 1 1] quad text{→ 1 row, 3 columns}$$

• Identical Matrix (probably meant "Identity Matrix") → has 1s on the diagonal and 0s elsewhere (square matrix).