Es sei \( B_{1}=\left\{\dot{e}_{1}, \dot{e}_{2}, \dot{e}_{3}\right\} \) die Standardbasis des \( \mathbb{R}^{3} \) und \( B_{2}=\left\{\dot{v}_{1}, \dot{v}_{2}, \dot{v}_{3}\right\} \) die Basis mit \[ \dot{v}_{1}=\left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right], \dot{v}_{2}=\left[\begin{array}{l}0 \\ 0 \\ 4\end{array}\right], \dot{v}_{3}=\left[\begin{array}{c}3 \\ 0 \\ -3\end{array}\right] \] Weiter sei die lineare Abbildung \( f: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3} \) durch die folgenden Bilder gegeben \[ f\left(\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]\right)=\left[\begin{array}{c}1 \\ -6 \\ 1\end{array}\right], f\left(\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]\right)=\left[\begin{array}{c}0 \\ 5 \\ -2\end{array}\right], f\left(\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right]\right)=\left[\begin{array}{c}2 \\ -1 \\ 4\end{array}\right] \] a) Berechnen Sie \( f_{B_{1}, B_{1}} \)

13 puntos Considere la transformación \( T: \mathbb{R}^{2} \rightarrow P_{3} \) definida por \[ T\binom{a}{b}=a+b+(a-b) x+(2 a+b) x^{2} \] a) 5 puntos Halle una base para el núcleo de \( T \) y su nulidad.

Q1. What is the best way of dealing with a hazard to ensure others are not put at risk? (a) Remove it immediately (b) Leave it for others to sort out (c) Enclose the area with caution tape (d) Display a notice or warning sign Q2. The legal responsibilities of an employer with regards to health and safety include what? (a) Charging employees for damaged or lost PPE (b) Provide safe work systems for employees (c) Provide insurance for dangerous work (d) Assign dangerous tasks to specific employees

Q6. Why do we investigate accidents? Pick all that apply (a) To avoid repeating (b) To find root cause (c) To place blame on someone (d) All of the above Q7. What is the purpose of a Job Safety Analysis (JSA)? (a) To identify potential hazards on construction sites (b) Monitor employee performance (c) Analyze project profitability (d) Conducting equipment and machinery inspection Q8. Which of the following is an example of a fall protection system in construction? (a) Safety glasses (b) Hard hats (c) Guardrails (d) Ear muffs

Q13. Which of the following hazards do you need to be aware of in roadside work zones? (a) Traffic (b) Weather (c) Poor lighting conditions (d) Work vehicle or machinery Q14. What is the major function of a water distribution system? (a) To carry water from a homie to a treatment plant (b) To carry water from a source to a pump house (c) To carry water from a treatment plant to a home (d) To carry water from a source to a filtration unit Q15. What is the recommended minimum distance to maintain from heavy machinery in operation? (a) 1 ft (b) 5 ft (c) 10 ? (d) 20 ft

Q9. What does the term "excavation" refer to in construction safety? (a) The process of removing debris from a construction site (b) The digging of trenches/foundation pits (c) The transportation of construction materials (d) A method to treat unstable slopes Q10. Which of the following is a safe practice for handling hazardous materials in construction? (a) Storing near heat sources (b) Storing near other hazardous materials (c) Using appropriate containers and labels (d) Storing near machinery Q11. Which of the following is a safe practice for operating heavy machinery in construction? (a) Operating with limited training (b) Ignoring safety signs (c) Inspect machinery before use (d) Multitasking while operating Q12. What is the purpose of a safety training program in construction? (a) To educate workers on construction techniques (b) To promote teamwork and collaboration (c) To enhance productivity and efficiency