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已知||=1,||=,且⊥(﹣),则向量与向量的夹角为( )
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高三下学期数学《》真题及答案
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已知向量a和向量b的夹角为135°|a|=2|b|=3则向量a和向量b的数量积a·b=_______
已知非零向量abc满足a+b+c=0向量ab的夹角为120°且|b|=2|a|求向量a与c的夹角
已知向量a与向量b的夹角为30°|a|=2|b|=那么向量a和向量b的数量积a·b=.
已知非零向量abc满足a+b+c=0向量ab的夹角为120°且|b|=2|a|则向量a与c的夹角为_
已知向量ab夹角为45°且|a|=1|2a-b|=则|b|=________.
已知向量ab夹角为45°且|a|=1|2a-b|=则|b|=________.
已知向量ab满足a+2b·a-b=-6且|a|=1|b|=2则a与b的夹角为____________
已知向量a与b的夹角为120°且|a|=|b|=4那么a・b的值为.
已知向量ab的夹角为60°且|a|=2|b|=1则向量a与a+2b的夹角等于________.
已知向量ab满足|a|=1|b|=4且a·b=2则a与b的夹角为________.
已知单位向量e1与e2的夹角为α且cosα=向量a=3e1-2e2与b=3e1-e2的夹角为β则co
已知|a|=1|b|=且a⊥a-b则向量a与向量b的夹角是________.
已知向量a与b的夹角为60°且a=-2-6|b|=则a·b=________.
已知向量m=λ+11n=λ+22若m+n⊥m-n则向量mn的夹角的余弦值为________.
已知向量a=10b=11则Ⅰ与2a+b同向的单位向量的坐标表示为____________Ⅱ向量b-3
已知向量ab满足a+2b·a-b=-6且|a|=1|b|=2则a与b的夹角为________.
已知向量a和向量b的夹角为30°|a|=2|b|=3则向量a和向量b的数量积ab=_______
已知向量a和向量b的夹角为30°|a|=2|b|=3则向量a和向量b的数量积a·b=.
已知向量ab的夹角为60°且|a|=2|b|=1则向量a与向量a+2b的夹角等于
150°
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已知单位向量e1与e2的夹角为α且cosα=向量a=3e1-2e2与b=3e1-e2的夹角为β则co
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6分ThatMondaymorningfeelingcouldbeacrushingpaininthechestwhichleavesyousweatingandgaspingforbreath气喘吁吁.RecentresearchfromGermanyandItalyshowsthatheartattacksaremorecommononMondaymorningsanddoctorsblamethestressofreturningtoworkaftertheweekendbreak. Theriskofhavingaheartattackonanygivendayshouldbeoneinsevenbutasix﹣yearstudyhelpedbyresearchersattheFreeUniversityofBerlinofmorethan2600Germansshowedthattheaveragepersonhada20percenthigherchanceofhavingaheartattackonaMondaythanonanyotherday. WorkingGermansareparticularlynotprotectedagainstattackwitha33percenthigherriskatthebeginningoftheworkingweek.Non﹣workersbycomparisonappeartobenomoreatriskonaMondaythananyotherday. Astudyof11000Italiansproved8a.m.onaMondaymorningasthemoststressfultimefortheheartandbothstudiesshowedthatSundayistheleaststressfuldaywithfewestheartattacksinbothcountries. ThefindingcouldleadtoabetterunderstandingofwhatistheimmediatecauseofheartattacksaccordingtoDrStefanWillichoftheFreeUniversity.Weknowalotaboutlong﹣termriskfactorssuchassmokingandcholesterol胆固醇butwedon'tknowwhatactuallycausesheartattackssowecan'tgiveclearadviceonhowtopreventthemhesaid. Mondaymorningshaveadoublehelpingofstressfortheworkingbodyasitmakesarapidchangefromsleeptoactivityandfromtherelaxingweekendtothepressuresofwork. Whenpeoplegetuptheirbloodpressureandheartrategoupandtherearehormonal内分泌changesintheirbodiesWillichexplained.A1thesethingscanhaveanunfavorableeffectinthebloodsystemandincreasetheriskofaclot血凝块whichwillcauseaheartattack. Whenpeoplereturntoworkafteraweekendoffthepaceoftheirlifechanges.TheyhaveahigherworkloadmorestressmoreangerandmorephysicalactivitiessaidWillich. 32.Mondaymorningfeelingasthispassageshows. A.isnotasseriousaspeoplethought B.isthefirttkillerinGermanyandItaly C.iscreatedbyresearchersinGermanyandItaly D.isharmfultoworkingpeopleinthecountriessurveyed 33.Toprotectpeoplefromaheartattackdoctorshavepaidmuchattentionto. A.people'sworkingtime B.people'slivingplace C.people'sdietandlifestyle D.people'snationalities 34.ItcanbelearnedfromthispassagethattheheartattackhassomethingtodowithallthefollowingEXCEPT. A.bloodpressure B.heartrate C.hormonalchanges D.bloodtype 35.IftheresearchersgiveussomeadvicetoavoidMondaymorningfeelingwhatmightitbe? A.Improveworkingconditions. B.NevergotoworkonMondays. C.StaywithadoctoronMondays. D.TakemedicinesonMondaymornings.
1分指出下列句子中划线部分在从句中的成分.回答可写汉字 TheschoolwherehestudiedisinShenzhen..
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15分Chessiscalledthegameofking.Itisatwo﹣playergame.Oneplayerusesthewhitepieces.The61usestheblackpieces.Eachpiecemovesinaspecialway.Onepieceisnamedtheking.Eachplayerhasone.Theplayerstaketurns62movetheirpieces.Ifaplayerlandsonapieceheorshetakesit.Thegameendswhenaplayerloseshisorherking.Thereareafewmore63rulebutthosearethebasics. Somepeoplethinkthatchessis64thanagame.Theythinkthatitmakesthemindstronger.Goodchessplayersusetheirbrains.Theythinkabout65willhappennext.Theseskillsarevery66useinlifeandinchess.Chessiskindoflikeaworkoutforthemind. Chessisnotjustforpeople.Computers67playchesssincethe1970s.atfirsttheymademistakes.Astimeswent68theygrewstronger.In1997acomputerbeat69bestplayerintheworldforthefirsttime.Itwasacomputer70callDeepBlue.Chesssurehascomealongway.Don'tyouthinkso? 61. 62. 63. 64. 65. 66. 67. 68. 69. 70.
1分…ButnoEricwhydidn'ttheyaskmewhathappened85shoutingatme?
8分Researchersmayhavediscoveredaperfectmaterialofdieting﹣lowfatcakeandcheese.Britishresearcherssaytheyhavecreatedaprotein蛋白质thatcanreplacefatperfectly. Theproteinswillenablefoodproducerstoremovemuchofthefatusedintheirproductsbutwithoutreducingproductquality. FundedbyteamfromUniversityofEdinburghtheresearchershaveproducedthemodified调整了的proteinsthateasilybreakdownandthereforeworknearlythesameasthefatsdoduringfoodproduction. We'vepavedthewayforthedevelopmentofmodifiedproteinsthatcanbeusedtoproduceawiderrangeofappealinglow﹣fatfoodssaidDr.SteveEustonwholedtheresearch.TheresultcouldbeimportantforhealthbenefitsaswellasareductionintheburdenontheNationalHealthServiceNHScausedbymanyweight﹣relatedhealthproblems. Protein﹣for﹣fatsubstitution替代品isnotacompletelynewideabuttodateithasbeenlimitedtoproductssuchasyogurts. Incheesesandcakesithasprovedlesssuccessfulinensuringtheoriginaltasteandtexturefundamentaltoconsumersatisfactionmainlybecauseproteinscouldnotmimicthebehavioroffatscloselyenough. Bystudyingtheproteins'chemicalstructuretheteamhasdevelopedadetailedunderstandingofhowproteinsbehavewhentheyareheatedorgothroughotherfoodproducingprocesses. Theproteinscouldencouragedevelopmentofawiderchoiceoflow﹣fatfoodshelpingconsumerstoeatmorehealthilyandreducingweight﹣relatedhealthproblems. Theteamhasachievedparticularlypromisingresultsinusingproteinstoreplaceeggswhichiscommonlyusedinbakeryitems. Suchsubstitutionnotonlycutsfatcontentbecauseeggscanbesubjecttosharpchangesinprice.Itcouldalsocutthecostproductsandsoencourageconsumerstoeatmorehealthily. 32.Whatcanwelearnfromthepassage? A.TheNHSwillbenefitfromthisnewfinding. B.Theresearchteamisfundedbyfoodproducers. C.Proteinforfatsubstitutionisacompletelynewidea. D.Productsofmodifiedproteinshavebeenputonsale. 33.Theunderlinedwordmimicmeans. A.reduceB.makeC.removeD.imitate模仿 34.Thesenewproteinsworknearlythesameasthefatsdobecause. A.theywillcutfatcontenteasily B.theywillbreakdowneasily C.theirproductsarecheaperandhealthier D.theyensuretheoriginaltasteandtexture 35.Whichofthefollowingisthebesttitle? A.ASpecialProtein B.HowProteinsWork C.CutDowntheFoodCost D.ASpecialResearchTeam.
4.5分SeaLifeMelbourneAquarium水族馆 Theall﹣newSeaLifeMelbourneAquariumsituatedintheheartofMelbourne'sCBDisoneofVictoria'sleadingvisitorattractionsandanunforgettableoutingforthewholefamily.Having12amazingzonesofdiscoverySeaLifeMelbourneAquariumistheveryplacethatyoucannotmisswhenyouvisitthecity. ♦OpeningTimes SeaLifeMelbourneAquariumisopenfrom930a.m.until600p.m.everydayoftheyearincludingpublicholidays.Lastadmissionisat500p.m.onehourbeforeclosing. ♦Location位置 SeaLifeMelbourneAquariumislocatedonthecornerofFlindersStreetandKingStreetMelbourne.ItissituatedontheYarraRiveroppositeCrownEntertainmentComplex. ♦GettingtoSeaLifeMelbourneAquarium Train SeaLifeMelbourneAquarium/ashortwalkfromeitherFlindersorSouthernCrosstrainstations. Tram有轨电车 TheSeaLifeMelbourneAquariumtramstopislocatedonthefreeCityCircleTramroute公交线路andalsoroutes70and75.CityCircleTramsrunevery10minutesinbothdirections. ShuttleBusTheMelbourneCityTouristShuttleisafreebusservicestoppingatkeytouristattractionsinandaroundtheCity.Runningdailyevery15minutesfrom1000a.m.to400p.m. ♦CarParking WhilethereisnopubliccarparkingatSeaLifeMelbourneAquariumthereareseveralpubliccarparkinglotsavailableonlyashortwalkaway. ♦WheelchairAccess SeaLifeMelbourneAquariumprovidespeopleinwheelchairswithfullaccesstoall12zones.Eachflooralsohaswheelchairaccessibletoilets. ♦Terms Ticketswillbeemailedtoyouimmediatelyafterpurchaseoryoucandownloadandprintyourticketsoncepaymenthasbeenaccepted.PleaseprintallticketspurchasedandpresentatthefrontentranceofSeaLifeMelbourneAquarium.Noticketnoentry! 25.SeaLifeMelbourneAquarium. A.islocatedatthecenteroftheCBDinthecity B.has12mostattractiveplacesinMelbourne C.admitsvisitorsfrom930a.m.until600p.m. D.isbesideCrownEntertainmentComplex 26.GettingtoSeaLifeMelbourneAquariumvisitorscantake. A.trainsfromSouthernCrosstrainstation B.shuttlebusesaroundthetrainstation C.boatsacrosstheYarraRiver D.eithertramroute70or75 27.SeaLifeMelbourneAquariumoffersvisitors. A.freecarparking B.wheelchairaccess C.Internetconnection D.transportationservice.
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10分Therearesomeverygoodthingsaboutopeneducation.Thiswayofteachingallowsthestudentstodeveloptheirowninterestsinmanysubjects.Openeducationallowsstudentstoberesponsiblefortheirowneducation.Somestudentsdobadlyintraditionalclassrooms.Theopenclassroommayallowthemtoenjoylearning.36Theywillnothavetoworryaboutgradesorrules.37Forsomestudentstherearetoofewrules.Thesestudentswilldolittleinschool.Theywillnotmakegooduseofopeneducationwhichissodifferentfromtraditionaleducation.Thesestudentsmayhaveaproblemofgettingusedtomakingsomanychoices.38Theyworryabouttherulesevenwhentherearenorules.Evenafewruleswillhelpthiskindofstudents.Thelastpointaboutopeneducationisthatsometraditionalteachersdonotlikeit.39Teacherswhowanttohaveanopenclassroommayhavemanyproblemsattheirschool. Younowknowwhatopeneducationis.Someofitsgoodpointsandbadpointshavebeenexplained.Youmayhaveyourownopinionaboutopeneducation.Thewriterthinksthatopeneducationisagoodideabutonlyintheory.40Ibelievethatmoststudentsbutofcoursenotallstudentswantsomestructureintheirclasses.Theywantandneedtohavesomerules.Insomecasestheymustbemadetostudysomesubjects.Manystudentsarepleasedtofindsubjectstheyhavetostudyinteresting.Theywouldnotstudythosesubjectsiftheydidnothaveto. A.Manyteachersdonotbelieveinopeneducation B.Openeducationisbetterthantraditionaleducation. C.Butmanystudentswillnotdowellinanopenclassroom D.Somestudentswillbehappierinanopeneducationschool E.Theteachers'feelingandattitudesareimportanttothestudents. F.Infactitmaynotworkverywellinarealclassorclass G.Formanystudentsitisimportanttohavesomerulesintheclassroom. 36. 37. 38. 39. 40.
25分最新调查指出人际关系正越来越被人机关系所取代甚至有网友调侃世界上最远的距离是我在你面前而你在低头看手机.根据以下要点用英语写一篇短文给21世纪英文报投稿. 1.描述这一现象2.分析其原因及弊端3.你认为该如何改变现状 注意1.词数120左右2.可适当增加细节使行文连贯.
8分ThereisnoquestionthatfewerteenagersareontheroadsintheUS. In197850%of16﹣year﹣oldshadgottheirfirstdrivinglicence.In2008accordingtotheUSTransportationDepartmentitwasjust30%.Thenumberofthoseaged19andunderwithdrivinglicenceshasalsobeendecliningsince1978when11989000hadlicence.In2010itwas9932441or4.1%ofAmericandrivers. IntheUK683273teenagershavedrivinglicences﹣just1.85%oftotallicenceholdersaccordingtoDepartmentofTransportfiguresfromSeptember2010. ButthedeclineintheUSmayhavemoretodowithtoughertestsandtheintroductionofthenewruleinmanystateswhichforcedriversagedunder16tobeaccompaniedbylicenseddriversof21yearsandolderwhendrivingthanthegrowthofsocialnetworking. InrecentyearstheannualnumberofjourneysbeingmadebyAmericandriversofallageshasdeclinedclearlyforthefirsttimeever.Carusebeganfallingin2007whenaveragepetrolpricesalmostdoubledto$4.12agallonandtheeconomybecameworse. ButtherearesignsthatAmericanremainsacountryonwheels.Ithasahighernumberofcarsperheadofpopulationthananyothercountryintheworld. CarswillalwaysbeapopularmeansoftransportationinAmerica.Youhavetotakeintoconsiderationsomeplacesdon'thaveaccesstopublictransportation.CarsaretheonlywaysomepeoplecangetaroundsaysKristinNevels.Thismakesdrivingnecessaryinsomeruralstateswhereabouttwiceasmanyteenagersareontheroadthaninbigcities. 29.Whatwouldbethebesttitleforthetext? A.DrivingintheUS. B.TransportationintheUS. C.USTeenagersDriveLess. D.PeopleLikeCarsintheUS. 30.whichofthefollowingisnotthereasonwhycarsareusedlessthanbefore? A.trafficjams B.hardertests C.expensivepetrol D.worsteconomy 31.WecanlearnfromthelastparagraphthatKristinNevels. A.doubtsthepopularityofthecaruseinthefuture. B.thinksAmericanpeoplecanlivewithoutcars. C.holdsconfidentattitudetothecars'useinAmerica. D.believesAmericashouldbuildupitspublictransportation. 32.Whatcanbeinferredfromthetext? A.TheUKhasmoreteenagerdriversthantheUS. B.A15﹣year﹣oldboycannotdrivealoneintheUS. C.TheUShasverydevelopedbustransportationsystem. D.BigcitieshavemoreteenagerdriversthanruralareasintheUS.
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8分Usuallywhenyourteacherasksaquestionthereisonlyonecorrectanswer.Butthereisonequestionthathasmillionsofcurrentanswers.ThatquestionisWhat'syourname?Everyonegivesadifferentanswerbuteveryoneiscorrect. Haveyoueverwonderedaboutpeople'snames?Wheredotheycomefrom?Whatdotheymean? People'sfirstnamesorgivennamesarechosenbytheirparents.Sometimesthenameofagrandparentorothermemberofthefamilyisused.Someparentschoosethenameofawell﹣knownperson.AboycouldbenamedGeorgeWashingtonSmithagirlcouldbenamedHelenKellerJones. Somepeoplegivetheirchildrennamesthatmeangoodthings.ClarameansbrightBeatricemeansonewhogiveshappinessDonaldmeansworldrulerLeonardmeansasbraveasalion. Theearliestlastnamesorsurnamesweretakenfromplacenames.AfamilywiththenameBrookorBrooksprobablylivednearbrook小溪SomeonewhowascalledLongstreetprobablylivedonalongpavedroad.TheGreenwoodfamilylivedinornearaleafyforest. Otherearlysurnamescamefrompeople'soccupations.ThemostcommonoccupationalnameisSmithwhichmeansapersonwhomakesthingswithironorothermetals.Inthepastsmithswereveryimportantworkersineverytownandvillage.SomeotheroccupationalnamesareCarter﹣apersonwhoownedordroveacartPotter﹣apersonwhomadepotsandpans. TheancestorsoftheBakerfamilyprobablybakedbreadfortheirneighborsintheirnativevillage.TheCarpenter'sgreat﹣great﹣great﹣grandfatherprobablybuilthousesandfurniture. Sometimespeoplewereknownforthecoloroftheirhairorskinortheirsizeortheirspecialabilities.WhenthereweretwomenwhowerenamedJohninthesamevillagetheJohnwiththegrayhairprobablybecameJohnGray.OrtheJohnwhowasverytallcouldcallhimselfJohnTallman.JohnFishwasprobablyanexcellentswimmerandJohnLightfootwasprobablyafastrunneroragooddancer. Somefamilynamesweremadebyaddingsomethingtothefather'sname.English﹣speakingpeopleadded﹣sor﹣son.TheJohnsonsaredescendantsofJohntheRobertsfamily'sancestorwasRobert.IrishandScottishpeopleaddedMacorMcorO.PerhapsalloftheMacDonnellsandtheMcDonnellsandtheO'DonnellsaredescendantsofthesameDonnell. 24.WhichofthefollowingaspectsdothesurnamesinthepassageNOTcover? A.Placeswherepeoplelived. B.People'sstatus. C.Talentsthatpeoplepossessed. D.People'soccupations. 25.AccordingtothepassagetheancestorsoftheCarpenterfamilymostprobably. A.ownedordroveacart B.madethingswithmetals C.madekitchentoolsorcontainers D.builthousesandfurniture 26.SupposeanEnglishcouplewhoseancestorslivednearaleafyforestwantedtheirnew﹣bornsontobecomeaworldleaderthebabymightbenamed. A.BeatriceSmith B.LeonardCarter C.GeorgeLongstreet D.DonaldGreenwood 27.Theunderlinedworddescendantsinthelastparagraphmeansaperson's. A.latergenerations B.friendsandrelatives C.colleaguesandpartners D.latersponsors.
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.5分Everythinghedidseemedreasonable.
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