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第一节One possible versionDear Sir/MadamKnowing the International Book Fair will be held nextweek in our city and that some volunteers are needed. I amwriting to recommend myselfThe following are my advantages. First of all, I speakEnglish so fluently that I have no difficulty communicatingwith foreigners. Secondly, as a monitor, I always organizeall kinds of social activities. More importantly, I am a reg-stered volunteer, so I have gained rich experience in volentering.I would appreciate it if I were given a chance. Lookingforward to your early reply.Yours.Li Hi第二节One possible versionLater that evening, my son came up to me, his handbehind his back. "I have something for you, Daddy, "hesaid. Beyond my expectation, he handed me a KenGriffey, Jr. card. He'd taken a pair of scissors and cutone copy of the Griffey off from the box. Now you don'thave to look for it anymore, "he said. Hearing what hesaid,I was shocked, and moved to tears. At once, the hugI gave him was the best price I ever paid for a cardI continued collecting, and even ended up buying andselling some old and valuable cards. However, there wasone card that I would never trade, which was a KenGriffey, Jr. card. Up to now, I still keep that Griffey, Jrcard, even if it has had the rough borders and the shabbycorners, and there is only a plain and simple board on theback. That is because that card. to me, is what baseball isall about. More importantly, it's also what loveall about
18.【解析】(1)证明:连接BQ,由题意知PD⊥平面BMQN,所以BQ⊥PD,生正2分因为在△PBD中,BD=PB=PD=22,所以Q为PD的中点,…因为PE=3ED,所以DE=40D=PD=DE=0=PD= m=0= 03分即QE=ED5分因为B0=OD,所以OE∥BQ,…6分因为OE平面BMQN,所以OE∥平面BMQNPC PD2-CD2_(22)2 (222)-4(2)在△PCD中,cos∠CPD=2×22×22在Rt△PNQ中,∠NQP=,cos∠QPN=所以PN=CN=PC-PN=7分即点N为线段PC上靠近C的三等分点以O为原点,建立如图所示的空间直角坐标系则0(0,0,0),A(0,-2,0),B(2,0,0),C(0,2,0),D(-2,.0,0),P(0,0,6),分(-2=(-2,-236)48=(,2,0A=(0,设平面PAB的法向量为n=(x,y,z),=0则取z=1,n=(3,-3,1)10分√2取z=1,n=(3,-3,1)……10分y √6z=0设直线NQ与平面PAB所成角为6则0=1c0,m>}=m0。6…11分综上,直线M0与平面PAB所成角的正弦值为点12分