5.On Sunday, President Trump signed a S900 billion relief appropriation, which calls for $600 direct payments to Americans. The president initially said he would not approve the measure, motivated by resistance rooted partially in the size of the direct payments. He has, however, continued to advocate for increasing those payments to $2,000, and Democrats largely agree. Some Republicans, however, are wary of ballooning federal spending figures (29 December 2020, FOXBusiness). (8 分)

6.A few months from now, a factory in South Africa is expected to begin churning out a million doses of Covid-19 vaccine each day in the African country hardest-hit by the pandemic. But those vials will probably be shipped to a distribution center in Europe and then rushed to Western countries that have pre-ordered them by the hundreds of millions. None have been set aside for South Africa (28 December 2020, New York Times). (8分)

7.Officials in China's Zhejiang province are racing to meet five-year energy consumption targets set by the central government that are due to expire on December 31. Earlier this month, a local directive instructed businesses to stop elevators below the third floor, and to only use heating when temperatures outside fell below 3 degrees Celsius (37 degrees Fahrenheit) (26 December 2020, CNN Business). (8 分)

8.Over the last few years, our understanding of the impacts of anthropogenic activities on marine biodiversity has increased. Science and technology have opened up new frontiers in the oceans. What was once regarded as featureless, unchanging and inexhaustible is now known to be complex, dynamic and finite. These same advances are also increasing human impacts on remote, deep and little known areas. Once limited largely to shipping and high seas fishing, commercial activities at sea are expanding rapidly and plunging ever deeper. Deep sea fishing, marine scientific research and energy development, are already taking place at significant depths. Military operations and seismic exploration have also intensified throughout the oceans, with growing impacts on deep water and high seas ecosystems and biodiversity. While the prospects of commercial deep sea bed mining are still uncertain, efforts worldwide to develop the deep sea resources facilitated by advances in technologies are likely to grow more systematically (UN General Assembly, A/62/66/Add.2, page 8-9).(20分)

9. Marine debris, including plastics and microplastics (MDPMs), is considered "a global concern affecting all the oceans of the world". It has been observed everywhere: from coastal areas to remote areas far from any anthropogenic pollution sources； from surface waters throughout the water column to the deep water and ocean sediments； and from the equator to the poles, including trapped in sea ice. In the intervening years, however, marine debris has not only increased exponentially, but also become characterized by the growing presence -- and now prevalence -- of non-organic and non- biodegradable components, in particular plastics. An estimated minimum of 5.25 trillion plastic particles weighing 268,940 tons are currently floating in the world's oceans. These figures do not include plastics accumulating on beaches or the sea floor, trapped in sea ice or ingested by organisms, all of which may partly explain the tremendous loss of microplastics observed from the sea surface compared with expected rates of fragmentation (UN General Assembly, A/71/74, page 3).(20分).

10. Piracy and armed robbery against ships remained a major threat to maritime security. While there was an approximate 13.5 percent reduction in reported actual and attempted acts worldwide in 2019 as compared to 2018, the first half of 2020 witnessed an approximate 20 percent increase in incidents as compared to the same period in 2019, with an almost twofold increase in Asia, which may be attributed partly to the challenges posed by COVID-19. Globally, the areas most affected by piracy and armed robbery against ships were West Africa (67 incidents), the Straits of Malacca and Singapore (45 incidents) and the South China Sea (34 incidents). While no incidents of piracy or armed robbery against ships were reported in waters around the Somali coastline, Somalia-based pirates continued to present a potential threat to international shipping. Of particular concern was the continued personal risk to seafarers in 2019, with 134 persons kidnapped and 59 persons taken hostage. In the first half of 2020, 54 persons were kidnapped and 23 persons were taken hostage. Approximately 90 percent of the kidnapping incidents occurred in the Gulf of Guinea (UN General Assembly, A/75/340, page 8). (20 分)

(a) Solve x2 y"-xy-3y= x2 by undetermined coefficients and variation of parameters respectively. (10%)

(b) y"+4y=g(x), y(0)=1,y'(0)=2 (10%) [Hint]: Solve this problem on two intervals, and then find a solution so that y and y' are continuous at x=π/2.

(a) Evaluate the net outflow rate of V across a sphere x+ y +2'=4 (10%)

(b) What is the outflow rate across the upper hemi-sphere x2 + y2 +z2=4 、 z ＞0 and the lower hemi-sphere x2+y2+z2=4 、z＜0,respectively. (10%)

(a)(6%)

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