三、韌性社區是本（第三）期災害防救深耕計畫推動的重點之一。在推動社區防災工作時，專業團隊應對社區進行哪些自然環境與社會環境分析？為何需進行這些分析？

四、發生大規模災害後，政府須提供短期避難安置（公設收容場所）服務協助受災居民。不過，地震後不久，主管單位尚不及進行詳細調查，需透過其他災情資料進行需求推估。在進行短期避難安置需求推估時，需掌握哪些資料？如何運用這些資料進行需求推估？（提示：常見的推估方法在第一階段推估離家戶數，第二階段推估前往公設收容所的人數）

1. What is the change in entropy of 500 g of water as its temperature increases from 10 °C to 25 °C?(1) ___ J/K ? (The specific heat of water is 4.19 kJ/(kg·K).)

2. The plates of a parallel-plate capacity carry surface charge density σ C/m². A dielectric slab of thickness t and dielectric Constant κ is inserted into the parallel plate capacitor with plates of area A, separated by distance d, as shown in Fig.1. Assume that the battery is disconnected before the slab is inserted.What is the total potential difference between the plates? (2) ___ V.What is the capacitance C₁ between the plates? (3) ___ nF.If the dielectric slab is replaced by a metal sheet with the thickness t, compared to the capacitance C₁, how is the capacitance affected? (increase? decrease? or keep constant?) (4) ___(Take d = 1 cm, t = 0.3 cm, σ = 2 nC/m², κ = 5, A = 40 cm², ε₀=8.85×10⁻¹² F/m.)

3. A long, straight wire carries a constant current I. A metal rod of length L moves at velocity v relative to the wire, as shown in Fig. 2. What is the potential difference between the ends of the rod? (5) ___

4. A dipole with a dipole moment p is pivoted freely at its midpoint. It lies in a uniform field. If its moment of inertia about the center is I, what's the angular frequency ω of the dipole oscillations for small angular displacements? (6) ___

5. A Cu strip of thickness 0.75 cm carrying a current of 10 A is set normal to a magnetic field. The Hall potential difference is 1.2 μV. What is B? (7) ___ T. (Take n = 8.5 × 10²⁸ electrons/m³)

6. A long solenoid of length l and cross-sectional area A has N turns. Find its self-inductance. (8) ___(Assume that the field is uniform throughout the solenoid.)

7. A small ball of mass m starts from rest at the top of a solid sphere of radius r and slides down its frictionless surface (see Fig. 3). At what angle θ will the small ball leave the sphere? (9) ___Calculate the speed v of small ball when it leaves the sphere. (10) ___

8. (a) Determine the coordinate for the center of mass (CM) of a uniform cone of height h and radius R, as shown in Fig. 4: (11) ___(b) If this cone is not uniform with a z-dependent density ρ = ρ₀·z, determine its CM. (12) ___

9. A guitar player tunes the fundamental frequency of a guitar string to 440 Hz. What will be the fundamental frequency if she then increases the tension in the string by 15%? (13) ___ (Hz).What will it be if, instead, she decreases the length along which the string vibrates by sliding her finger from the tuning key one-fourth of the way down the string toward the bridge at the lower end? (14) ___ (Hz)

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