Why are people in many areas trying to reduce erosion? To create more beaches To prevent damage to infrastructure and farmlands To make the land flatter To stop the spread of nutrients

Which of the following statements islare TRUE of the major schools of economic thought? i. Keynesians believe in the use of macroeconomic tools to stabilise the economy whereas the others do not. ii. Monetarists believe that monetary policy is more effective than fiscal policy in eliminating unemployment, whereas Keynesians believe the opposite. iii. Supply-siders believe that incentives to work, save and invest are more important than macroeconomic demand manipulation in managing the economy. iv. The classical economists believed that the monetary and real sides of the economy wereentirely separate, whereas the other schools believe that the monetary sector can affecthe real economy, at least in the short run. a) i b) i and ii c) i, iii and iv d) ii, iii and iv

Calcola il prodotto tra i numeri complessi \( \quad z_{1}=8-i 6 \) e \( \quad z_{2}=-3+i 4 \quad \) e scrivi il risultato nella forma onenziale.

2. Sea \( T: P_{2} \rightarrow M_{22} \) la función definida por \[ T\left(c+b x+a x^{2}\right)=\left(\begin{array}{cc}b+c & a+b \\ a+b & b-c\end{array}\right) \] cuyas bases canónicas se denotan por \( B_{1} \) para \( P_{2} \) y \( B_{2} \) para \( M_{22} \). (a) Compruebe que \( T \) es una transformación lineal. (b) Determine la representación matricial de \( T \) y el nucleo de \( T \). (c) El rango y nulidad de \( T \).

Ex 4: Give the opposite a) A merciful king

3.20. Para \( n \in \mathbb{Z}^{+} \)se define \( f(n) \) como el número de enteros positivos \( <n \) que son primos relativos con \( n \), por ejemplo \[ \begin{aligned} f(1)=1, \\ f(2)=1, \\ f(3)=2, \\ f(4)=2\end{aligned} \] 3.20.1. Calcular \( f(10), f(13), f(18), f(24) \) \( \begin{array}{l}\text { 3.20.2. Para } n=12,18,19,25 \text { calcule } \\ \text { 3.20.3. Infiera una fórmula para } \\ \qquad\end{array} \)