**Answer:**

<em>**a = 10**</em>

<em>**b = 2.5**</em>

**Step-by-step explanation:**

The given vector is

<-1, 4>

Let represents <-1, 4>.

First, the **dilation **is done by a factor of **2.5.**

If the dilation of a vector <, > is done by a factor <em>k:</em>

Then the resulting vector becomes:

The resulting as per above explanation:

Now, it is given that the vector is rotated by or .

The steps to find the resulting vector after the rotation of or , we can use the simple method:

**Step 1:** Multiply the value with -1.

i.e. the vector now becomes <2.5, 10> (Negative sign of x value removed).

**Step 2:** Swap the values of and .

So, the resulting vector is:

<10, 2.5>

In other form, we can represent the above vector as:

Comparing with

<em>**a = 10**</em>

<em>**b = 2.5**</em>