6. Assume you are at an ice cream shop and you order a bowl of ice cream with 3 scoops. There are 8 flavors to choose from. How many different bowls of ice cream can you have? (Repetition of flavors in the bowl is allowed.)

Sea \( a \in \mathbb{R} \) y consideremos el subconjunto \( S=\left\{\left(1,1,2, a^{2}\right),(1,1-a, 2,0),(2,2-a, 6-a, 4)\right\} \) de \( \mathbb{R}^{4} \). Denotemos por \( U \) al subespacio generado por \( S \) en \( \mathbb{R}^{4} \). Señale todas las proposiciones verdaderas: \( \square \) a. El conjunto de vectores \( S \) es linealmente independiente para todo \( a \in \mathbb{R} \). b. Si \( a=0 \) entonces el conjunto de vectores \( S \) es linealmente dependiente. \( \square \) c. Si \( a=1 \) entonces el conjunto de vectores \( S \) es linealmente dependiente. \( \square \) d. Si \( a=-1 \) entonces el conjunto de vectores \( S \) es linealmente dependiente. e. Si \( a=0 \), la dimensión de \( U \) es \( \mathbf{1} \). f. Si \( a=2 \), la dimensión de \( U \) es 2. g. Si \( a=1 \), la dimensión de \( U \) es 3 .

You are a strategy consultant who has recently been engaged by a tertiary institution which is on the verge of rolling out a new, innovative and disruptive strategy. Practica advise the institution on the factors they should put in place to ensure that their new strategy is implemented successfully

What is the multiplier for calculating a 45 degree offset when conduit is being bent?

Explain the operation of a glow plug.

Diketahui \( A=\left[\begin{array}{ccc}0 & 0 & -2 \\ 1 & 2 & 1 \\ 1 & 0 & 3\end{array}\right] \). Tentukan nilai cigen dati matriks \( A \) dan basis untuk m ang eigen !