A water wheel has a radius of 11 feet. The wheel is rotating at 25 revolutions per minute. Find the linear speed, in feet per minute, of the water. The linear speed is approximately \( \square \) feet per minute. (Round to the nearest whole number as needed.)

\begin{tabular}{l} Exercise 2.5 \\ \( \begin{array}{lll}\text { 1. Express each of the following numbers as prime factorization form. } \\ \begin{array}{lll}\text { a. } 21 & \text { b. } 70 & \text { c. } 105\end{array} \\ \begin{array}{lll}\text { d. } 252 & \text { e. } 360 & \text { f. } 1,848\end{array} \\ \text { 2. } 180 \text { can be written as } 2^{a} \times 3^{b} \times 5^{c} \text {. Then, find the value of } a, b \text { and } c \text {. } \\ \text { 3. Find the four prime numbers whose product is } 462 .\end{array} \) \\ \hline\end{tabular}

Simplify. \( \begin{array}{lll}\text { 10. }(8 i)-(3 i) & \text { 11. }(-2 i)^{2} & \text { 12. }(7+2 i)-(3-4 i) \\ \text { 13. }(-2+i)^{2} & \text { 14. }(3 i)(2 i)-(3+5 i) & \text { 15. }(-3+4 i)(9-6 i)\end{array} \)

3 En blå flytlina är 954 centimeter lång. Den ska klippas i tre lika långa bitar. Hur lång blir varje bit?

Suppose that a country has a mixture of individuals and companies that are in each of the following situations: Group I. These have borrowed in domestic currency to finance assets whose values are also in domestic curren Group II. These have borrowed in foreign currency to finance assets valued in domestic currency. Group III. These have borrowed in domestic currency to finance assets valued in foreign currency. Group IV. These have borrowed in foreign currency to finance assets valued in (the same) foreign currency. Which of these groups see the domestic-currency value of their wealth fall when the country devalues? (Assume achese that the initial value of the assets is at least as great as what was borrowed).

1. If \( \vec{A}=2 \vec{\imath}+3 \vec{\jmath}, \vec{B}=3 \vec{\imath}-\vec{\jmath} \), then \( \|\overrightarrow{2 \mathrm{~A}}-\overrightarrow{\mathrm{B}}\|=\ldots \) 2. If \( \vec{A}=(-2,1), \vec{C}=(-3, k) \) are parallel, then the value of \( \mathrm{k}=\ldots \) 3. If \( \vec{A} \perp \vec{B}, \vec{A}=(3,4), \vec{B}=(4, m) \), then \( m=\cdots \). 4. If \( \vec{A}=(2,3), \vec{B}=(-1,2) \), then \( \overrightarrow{A B}=\cdots \) 5. If \( \vec{A}=\left(10,45^{\circ}\right) \), write \( \vec{A} \) in term of fundamental unit vectors. 6. If \( \vec{A}=(4,4 \sqrt{3}) \) find in polar form the position vector of the point A respect to the origin point. 7. If \( \|-8 \overrightarrow{\mathrm{~A}}\|=5\|k \overrightarrow{\mathrm{~A}}\|=\ldots \ldots \), then find the value of k