Materiales basicos de Física

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  –EÕO DLC MLJTLJEPKO DL AEMB\ VKMMB\ VEPE LC A\JDOKJ]TKT\TO VLDEHÝHKMO JEMKOJEC AOJTLPPKMO ” KVJA M\P]O 7 DKDÅMTKME DL CE NÁ]KME \JKDED KKK 7 DL]EPPOCCO DL MEVEMKDEDL] MKLJTÁNKME] ]L]KÝJ =*5 7 CE@OPETOPKO LRVLPKALJTEC DL NÁ]KME EMTK^KDED < 7 Kdljtknkmemkýj dl Aetlpkecl} @å}kmo} dl Ná} kme { ]lclmmký j dl Tëmjkme} vepe }| aejlgo MKMCO 7 K^ ]LDL 7 B\E\PE E\CE 7 ]!0 KJTL HPEJ TL] 7 HEPMÁE COWE# VE]M\EC OMBOE HEAEPPE# HLJJ[ ]EJTOAL CEJDE# DOPE \P@KWEHE]TLH\K @OPGE]# PO]EJE 5

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Page 1: Materiales basicos de Física

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–EÕO DLC MLJTLJEPKO DL AEMB\ VKMMB\ VEPE LC A\JDO‑

KJ]TKT\TO VLDEHÝHKMO JEMKOJEC AOJTLPPKMO ” KVJA

M\P]O 7 DKDÅMTKME DL CE NÁ]KME

\JKDED KKK 7 DL]EPPOCCO DL MEVEMKDEDL] MKLJTÁNKME]

]L]KÝJ =*5 7 CE@OPETOPKO LRVLPKALJTEC DL NÁ]KME

EMTK^KDED < 7 Kdljtknkmemkýj dl Aetlpkecl} @å}kmo} dl Ná}kme { ]lclmmkýj dlTëmjkme} vepe }| aejlgo

MKMCO 7 K^

]LDL 7 B\E\PE

E\CE 7 ]!0

KJTLHPEJTL] 7

HEPMÁE COWE# VE]M\EC

OMBOE HEAEPPE# HLJJ[

]EJTOAL CEJDE# DOPE

\P@KWEHE]TLH\K @OPGE]# PO]EJE

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VPONL]OPE 7 IEPKJ JE^EPPLTL DÁEWM\P]O7 DKDEMTKME K^! NÁ]KME ! AODECKDED E DK]TEJMKE\jkded =* Dl}eppocco dl ce} mevemkdedl} mkljtánkme}]l}kýj =*5* Ce`opetopko Lrvlpkaljtec dl Ná}kmeEmtk~kded =*5*<* Tpe`egejdo moovlpetk~ealjtlNkmbe dl tpe`ego 57 Kdljtknkmemkýj dl Aetlpkecl} @å}kmo} dl Ná}kme { ]lclmmkýj dl Tëmjkme}

vepe }| aejlgo*‑ 

K* EVPLJDKWEGL] L]VLPEDO]7o Kdljtknkme co} aetlpkecl} `å}kmo} dlc ce`opetopko dl Ná}kme*o Dk}mpkakje tëmjkme} ovlpetk~e} vepe pleckwep edlm|edealjtl l}t|dko} lj lc ce`opetopko*

KK* KJTPOD\MMKÝJ

¿L} vo}k`cl ce moavplj}kýj dl co} nljýaljo} jet|pecl} }kj vpåmtkme} dl ce`opetopko?

Ce} vpåmtkme} dl ce`opetopko moj}k}tej lj emtk~kdedl}

dl dl}m|`pkakljto dl blmbo}# mojmlvto} { cl{l}

aldkejtl lc |}o dl co} vpoml}o} dl ce mkljmke lj

}kt|emkojl} h|kede} vop lc vponl}op { }oj

kavpl}mkjdk`cl} vepe moavpljdlp co} nljýaljo}

ná}kmo} dlc ljtopjo jet|pec# moj lcco} }l nemkckte ce

edu|k}kmkýj dl be`kckdedl} mkljtánkme} { vojl e co}

l}t|dkejtl} lj }kt|emkýj dl pl}oc~lp vpo`clae}

vpåmtkmo}# vop tejto# lc ce`opetopko dl`l l}tep dotedo dl |je }lpkl dl kjnpel}tp|mt|pe} { dl

aetlpkecl}# ikt { lu|kvo} `å}kmo} u|l vo}k̀ kcktlj lc dl}eppocco dl ce} emtk~kdedl}

lrvlpkaljtecl}# vepe hepejtkwep lc cohpo dl l}to} vpový}kto}*

–L} u|l lj ce la`pkeh|lw dl moavpljdlp# ljtpe }klavpl ce eclhpáe dl }ljtkpjo} pl}voj}e`cl} dl ce} ~lpdedl} u|l dl}m|`pkao}‑ 

  Nkcý}ono7 Glej!Ve|c ]eptpl

† ¿Moj u|ë aetlpkecl} vodpë pleckwep |je dlao}tpemkýj dl tpej}ak}kýj dl mecop?† ¿M|åc dl co} aetlpkecl} jo} vlpaktl tpe`egep vepe dlao}tpep lc ao~kakljto mkpm|cep { ce

moj}lp~emkýj dl ce ljlpháe e ce ~lw?† ¿U|ë aetlpkecl} moavojlj lc ikt dl lclmtpo}tåtkme?

0

Nkmbe dl tpe`ego 57 Kdljtknkmemkýj dl Aetlpkecl} @å}kmo} dl Ná}kme { ]lclmmkýj dlTëmjkme} vepe }| Aejlgo*‑

¥L}te} }oj ech|je} dl ce} vplh|jte} u|l ~e} e pl}vojdlp kjtlpmea`kejdo

 

ovkjkojl} { }e`lpl} moj t| moa|jkded dl evpljdkwegl%¥Voj lj vpåmtkme co u|l l}tå} evpljdkdo }o`pl co} aetlpkecl} { co}lrvlpkaljto} lj lc m|p}o dl ná}kme# pl~k}e lc aej|ec dl ce`opetopko dl ná}kme dlt| K*L* o lj todo me}o# ljtpe e co} }kh|kljtl} ljceml} xl`# lj lcco} ljmojtpepå}kjnopaemkýj }o`pl ce dl}mpkvmkýj { |tkckded dl co} aetlpkecl} o lu|kvo}`å}kmo} dl Ná}kme* ¥]kj d|de pl}oc~lpå} lj nopae lrkto}e l}te nkmbe dl tpe`ego%

Clmt|pe} ovmkojecl} J¶ 7 =# 4 { <7=+ –Ikt dl lclmtpoaehjltk}ao! ALD! VLP\‑bttv7//mkljmkel}mocep*jlt/vpo{lmto}/xv!mojtljt/|vcoed}/0656/60/H\KE!65*vdn 4+ Lu|kvo} dl ná}kme hljlpec `å}kmo 7 Kaehlj# Dl}mpkvmkýj# { \tkckdeddl dknlpljtl} kj}tp|aljto} { lu|kvo}* Dom|aljto lj VDN*bttv7//xxx*~ljt|}mkljmke*moa/vdn}/metecoho_nk}kme_u|kakme*vdn <+ Mkljtkikt7 –Evepeto} l kj}tp|aljto} vepe lc ce`opetopko dl ná}kme‑*bttv7//xxx*mkljmkenemkc*moa/evepeto}dlce`opetopko*btac

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KKK* DL]EPPOCCO DL CE] EMTK^KDEDL]

5pe*Emtk~kded7 Plmojomkakljto dl co} Aetlpkecl} @å}kmo} dlc Ce`opetopko dl Ná}kme

 

e+ O`}lp~e { plmojoml mede |jo dl co} aetlpkecl} u|l e mojtkj|emkýj }l vpl}ljtej* L}mpk`llc joa`pl { ce |tkckded dl mede |jo dl lcco}*

Joa`pl7Mpojýaltpo Joa`pl7 vcejo kjmckjedo mojTpej}voptedop Joa`plaåu|kje dl Xbka}|pt 

\tkckded7Aldkp tklavo \tkckded7 Aldkp åjh|co} # lcl~ep co} m|lpvo} Hljlpedop lclmtpo}tetkmo dl ~octegl

Joa`pl7 @ejmo dl mecop "vkpýaltpo+ Joa`pl7 tlpaýaltpo m|edpejtl

\tkckded7 Dkcetemkýj }l co} }ýckdo} \tkckded7 akdl ce tlavlpet|pe \tkckded7 Ojde} }ojope}

]kj|}okdec

 

Joa`pl7 Eavlpáaltpo Joa`pl7 `o`kje }ocljokdl Joa`pl7 Lclmtpo}movko

\tkckded7 kjtlj}kded dl ce \tkckded7 Meavo aehjëtkmo |jknopal   Dltlmte meavo lcëmtpkmo

moppkljtl

=

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Joa`pl7 @otlccedlCl{dlj Joa`pl7 Hljlpedop dl ^ej Dlp Hpenn Tpej}nopaedop dl do} j÷mclo}

\tkckded7 ecaemlje mephe lcëmtpkme \tkckded7 em|a|ce mephe lcëmtpkme  \tkckded7 l} |j dk}vo}ktk~o u|l

Moj~klptl ce ljlpháe lcëmtpkme ectlpje dl

|j mklpto jk~lc }l tlj}kýj# lj ljlpháe

ectlpje dl otpo jk~lc dl tlj}kýj vop aldko

dl kjtlpemmkýj lclmtpoaehjëtkme*

Joa p̀l7 Ejkcco dl Hpe~l}ejdl* Joa p̀l7 ge|ce nepede{ Joa p̀l7 ̂ e}o} Moa|jkmejtl}

\tkckded7 Dkcetemkýj dl co} m|lpvo} \tkckded7 Lu|kck̀ pko lclmtpo}tåtkmo \tkckded7 vpl}kýj bkdpo}tåtkme

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Joa`pl7 IKT dl vl}e} Joa`pl7 Mecopáaltpo Joa`pl7 Vl}e} pej|pede}

\tkckded7 Aldkp ae}e \tkckded7 mecop kjtlpjo \tkckded7 vepe aldkp ae}e

Joa`pl7 @ecejwe ejecktkme Joa`pl7 mkckjdpo dk~lp}o} Joa`pl7 Dkjeaýaltpo

\tkckded7 Aldkp ae}e a|l}tpe} vl}o} \tkckded7 dk~lp}o} \tkckded7 akdl vl}o} lj J

M|`lte dl ojde} L}vlgo} ejh|cepl} Joa`pl7 Kaåj

\tkckded7 Dlao}tpemkýj dl ojde} lj eh|e \tkckded7 Plnclgep o`glto} "kaehlj ~kpt|ec+ \tkckded7 aehjltk}ao

<

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Almblpo @|j}lj Joa`pl7 Vocle Joa`pl7 ~e}o vplmkvktedo

\tkckded7 moa`|}tkýj \tkckded7 Aåu|kje} }kavcl} \tkckded7 akdl ~oc|alj*

Tljewe ek}cejtl poge O~kcco dl bkco Xkjmbe

\tkckded7 vepe co} lclmtpodo} \tkckded7 ~epkedo Aldkp cojhkt|d

 

Vëjd|co lclmtpo}tåtkmo Vpo`lte hped|ede Dk}mo dl Jlxtoj

\tkckded7 aldkp o}mkcemkýj "lclmtpkmkded+ \tkckded akdl ~oc|alj |tkckded7 Vepe vpod|mkp C|w ̀ cejme

>

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T|`o dl Jlxtoj Joa`pl7 L}nlpe dl Ve}mec Joa`pl7 Hco`o Vplj}e Aejoaëtpkme

Vepe meáde dl co} m|lpvo} \tkckded7 Vpkjmkvko dl Ve}mec \tkckded7 vpovkldedl} \tkckded7 vplj}e bkdpå|ckme

 

*

Joa`pl7 vëjd|co Aerxlcc Joa`pl7 Cljtl `k moj~lro Joa`pl7 ]ckji{\tkckded7 ck}týj vepe n|lpwe \tkckded7 ývtkme \tkckded vepedoge almåjkme*

 

Joa`pl7 tpoavo dl aedlpe Joa`pl7 Nomo lcëmtpkmo Joa`pl7 ]ka|cedop dl ojde}\tkckded7 Ao~kakljto dk}mo \tkckded7 Mkpm|kto lcëmtpkmo \tkckded7 dl}vceweakljto dl ce} ojde} bopkwojtecl}

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Tlpaýaltpo mcájkmo mojlmtopl} dl mo`pl Joa`pl7 Cljtl @k

mýjme~o

\tkckded7 Aldkp tlavlpet|pe mopvopec \tkckded7 kj}tecemkýj dl mkpm|kto} \tkckded7 dk}tejmke nomec

Joa p̀l7 Aockjltl lclmtpo}tåtkmo Joa`pl7 Vpk}ae} ývtkmo} Joa`pl7 plgk cce dl dknpemmkýj

\tkckded7 Ao~kakljto dl kojl} \tkckded7 dk}vlp}kýj dl ce c|w \tkckded7 }lvepe ce c|w

Joa`pl7 @ejmo ývtkmo Joa`pl7 ]ovoptl |jk~lp}ec Joa`pl7 ce}lp  

\tkckded7 Dl}vceweakljto dl ce c|w \tkckded7 Kj}tecep lu|kvo} \tkckded7 ]lõecep pe{o} dl c|w

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0de* Emtk~kded7 Dkecohejdo moj t| moa|jkded dl evpljdkwegl# }lclmmkoje co}aetlpkecl} dl ce emtk~kded ejtlpkop# |}edo} moj ae{op nplm|ljmke# lj lrvlpkaljto}

dl almåjkme# bkdpo}tåtkme# mecopkaltpáe# ojde} almåjkme} { lclmtpoaehjëtkme}#lclmtpo}tåtkme} { lclmtpodkjåakme} o lclmtpoaehjltk}ao* Jo plvkte} co} aetlpkecl}*

 

Almåjkme Bkdpo}tåtkme Mecopkaltpáe

Ojde}almåjkme}/ojde}lclmtpoaehjëtkme}

Lclmtpo}tåtkme

Lclmtpodkjåakme {lclmtpoaehjltk}ao

Lu|kvo

MojCk}týj vepe

n|lpwe

Aejýaltpo

Mecopáaltpo  

Vpk}ae

^OCTKALTPO Lclmtpokaej

Vocle}kavcl L}nlpe dl

ve}mec

Tlpaýaltpo @ejmo ývtkmo Hljlpedop dl^ej dl Hpenn 

N|ljtl dl vodlp 

Vceme dlempáckmo

^e}omoa|jkmejtl

Tlpaom|vce} Cå}lp Aåu|kje dlXbka}b|pt

A|ctáaltpo

Notokjtlpp|vtop dl c|w

kjnpeppoge

T|`o} dl~kdpko

Mecljtedop lcëmtpkmo

Aåu|kje dl ojde} Aockjltllclmtpo}tåtkmo

Pl}k}tljmke

Vcoaede Dk}mo} dlec|akjko

Dk}mo dl Jlxtoj Lclmtpo}movko Hec~ejýaltpo

Vëjd|co}kavcl

^epkccealtåckme

L}vlgo} vcejo} {l}nëpkmo}

Ge|ce dlNepede{

^e}o} moj `o`kje}

Plhce TLclmtpýnopo dl~octe

]lcljokdl

Aockjltl Aotop lcëmtpkmo

;

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=pe* Emtk~kded7 Plcemkoje aetlpkecl} o lu|kvo} dl ná}kme moj }|} moppl}vojdkljtl}tëmjkme} dl aejlgo*

Tkje o m|`lte dl ojde}* " g + e* Vepe u|l meph|l ce aåu|kje l} jlml}epko }lmep lcea`kljtl lj dáe} b÷aldo}*

Lclmtpo}movko " a + `* Dl`l mocomep}l mlpme ec hljlpedop vepe o`}lp~ep mýao hkpe* Moavp|l`e tea`këj ce} n|lpwe} dl emmkýj {plemmkýj*

Dk}mo dl Aerxlcc * " o + m* Dl`l mocomep}l }o`pl |je boge hped|ede vepemoavpo`ep lc åjh|co ljtpl co} l}vlgo} { }| plcemkýjmoj lc j÷alpo dl kaåhljl}*

T|`o dl Akioce* " n + d* Ce ae}e dl`l }lp }|}vljdkde vop lc hejmbo kjnlpkop#ce m|ec jo dl`l lrmldlp lc cáaktl dl lce}tkmkded dlca|lccl o pl}optl*

Ejkcco dl Hpe~l}ejtl* " cc + l* Mocomep lc tpoavo dl aedlpe lj ce veptl kjnlpkop dlctpkåjh|co { dlgepco podep*^e}o} Moa|jkmejtl}* " j + n* Aldkp lc tklavo u|l dlaope lj plmopplp ce `|p`|ge

ce} dk}tejmke} dl 56ma# 06ma#** 26ma…9 dl}dldk}tejmke mlpo# mede ~lw { moj vomo åjh|co dlkjmckjemkýj*

Hljlpedop dl ^ej DlHpenn*

" e + h* Dl`l mojlmtep}l lj }lpkl moj ce} pl}k}tljmke} {pleckwep ce} aldkmkojl} dl moppkljtl*

A|lccl vepe ojde}* " i + b* Dl`l tpe`egep}l lj |j ea`kljtl o}m|po { }o`pl |jeal}e `klj jk~lcede* ]|gltejdo `klj ce} cljtl}#vpk}ae} { nomo*

Aockjltl lclmtpo}tåtkmo* " ` + k* Dl`l mojlmtep}l lj vepeclco moj ce} pl}k}tljmke} {pleckwep ce} aldkmkojl} dl dknlpljmke dl votljmkec*

L}vlgo} ejh|cepl}* " m + g* Lmbep }o`pl ce m|`lte }ýco |j mljtáaltpo dl eh|e

Dkjeaýaltpo* " d +i* Dlgepco melp }o`pl lc vk}o { toaåjdoco dl ea`o}lrtplao} ehktep lj nopae ~lptkmec | bopkwojtec*

Eavlpáaltpo* " k +c* \}ep poj dl u|laep vepe mecljtep co} ecea p̀l}altåckmo}# }k ce eh|ge }l a|l~l# }khjknkme u|l ë}to} }ldkcetej ckjlecaljtl*

^octáaltpo* " h + cc* Mecljtep ce ̀ oce dl altec eclgåjdoco dlc ejkcco*

Vkpýaltpo dl m|edpejtl " c +

a* Mephep ce `oce dl vp|l`e moj ce aåu|kje dl ^ejDl Hpenn { emlpmep e l}tl kj}tp|aljto }kj tomepco vepemoavpo`ep }k l}tå o jo mephedo*

Vepedoge almåjkme* " l+ j* Lmbep eh|e mocoplede { vop lc t|`o dl ae{op dkåaltpo# jo ao~lp be}te ~lp lc jk~lc u|l ecmejwe lceh|e*

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¥Moclhe}%# plmopdlao} u|ë vpomldkakljto}pleckweao} m|ejdo aejkv|ceao} co} evepeto}o aetlpkecl} dlc ce`opetopko dl ná}kme# l}e}emmkojl} u|l jo} vlpaktlj lc cohpo dl co}evpljdkwegl} dl ce} vpåmtkme} moj}tkt|{lj ce}tëmjkme} dl aejlgo%*

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@ejmo ývtkmo* " b + o* Ljpldep tode ce vkte }o`pl lc dk}mo { dlgepco melp*

4te* Emtk~kded7 Pl}vojdl moj e{|de dl t| moa|jkded dl evpljdkweglce} }kh|kljtl} m|l}tkojl}*

5* Lj lc }kh|kljtl aojtegl }l l}tå moavpo`ejdo ce vpod|mmkýj dl ojde}almåjkme} l}temkojepke}# kjdkmep u|ë aetlpkecl} }l jlml}ktej vepe tec vpový}kto*

0* ¿U|ë Ikt plvpl}ljte ce kaehlj? L}mpk`l lc joa`pl dl < aetlpkecl}*

=* ¿U|ë vpkjmkvko }l moavp|l`e lj ce} kaåhljl}? [ ¿U|ë aetlpkecl} dlce`opetopko }l plu|klplj?

Lu|kck`pko Cl{ dl lav|gl

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Al}e dl tpe`ego# }ovoptl |jk~lp}ec# bkco# vl}e# vocle# pl}optl*

Pl}v|l}te7† Vocle}† Vl}e}† Dkjeaýaltpo† ]ovoptl \jk~lp}ec† Nege} { me`cl}

† Aojtegl dl n|lpwe lj lu|kck`pko

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Co} aetlpkecl} |}edo} }oj7 @ecejwe# vl}e}# nklc# dlvý}kto moj eh|e*

Lj ce }kh|kljtl nkh|pe ¿u|ë }l l}tå moavpo`ejdo? ¿L}mpk`l lc joa`pl dl 4 aetlpkecl}?

Pl}v|l}te}7]l l}tå moavpo`ejdo lc eavlpegl dl ce `o`kje `ego lc lnlmto dl |je `eppe dl kaåj

Aetlpkecl}7 @eppe dl kaåj# Eavlpáaltpo# `o`kje { me`cl

5* ¿Vop u|ë hkpe lc aockjltl lclmtpo}tåtkmo?

Pl}v|l}te7 Vop ce dknlpljmke dl ce n|lpwe} bkdpo}tåtkme}*

0* Ejeckwe ce kaehlj { l}mpk`l moj u|ë kj}tp|aljto dl ce`opetopko dlao}tpepáe} e t|} l}t|dkejtl}

co u|l }l o`}lp~e lj ce l}mlje*

 

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Pl}v|l}te7 CE L]NLPE DL VE]MEC

Moj co} ~e}o} moa|jkmejtl}*

MOJMC\]KOJL]Dkecohe moj t| moa|jkded dl evpljdkwegl { nopa|ce ech|je} mojmc|}kojl} }o`pl ce nkmbe dltpe`ego dl}eppoccede*† L} jlml}epko mojomlp ce |tkckded dl co} aetlpkecl} dl ce`opetopko dl ná}kme# vepe tpe`egep 

emlptedealjtl lj co} lrvlpkaljto}*† ]l be vodkdo kdljtknkmep tëmjkme} vepe }| aejlgo*† ]kp~l vepe ce lce`opemkýj dl h|áe} dl vpåmtkme} dl ce`opetopko dl Ná}kme*† ]l be vodkdo plmojomlp ce} mepemtlpá}tkme} { |tkckded dl co} aetlpkecl} `å}kmo} dl ná}kme*† Vlpaktl kjjo~ep co} mojomkakljto} dl Ná}kme*† ]l v|ldl lce`opep aetlpkecl} me}lpo} e veptkp dl ce} mepemtlpá}tkme} dl co} aetlpkecl}

l}t|dkedo}*

¥Nlckmktemkojl} vop lc tpe`ego pleckwedo% 

Vepe moavclaljtep t| kjnopaemkýj7

Ljtpe e co} }kh|kljtl} ljceml} xl`# ebá ljmojtpepå} lrmlcljtl kjnopaemkýj }o`pl aetlpkecl} {vpåmtkme} dl ce`opetopko7

bttv7//xxx*ejhlcnkpl*moa/tpli/`koaltpke{hljltkme/vpemtkme}*VDN bttv7//xxx*g|jtedlejdec|mke*l}/e~lppol}/z0;865402/mmjj/`ejmo5/Emtk~kded_etao}nlpe_5*vdn 

Dlao}tpemkojl} { vpåmtkme} dl ce`opetopko vepe lc domljtl lj7 bttv7//xxx*coplto*|jkmej*l}/KL]066</KL]M|p}o64*btac

@k`ckohpenáe7

† ECEA@KU\L 54 "5;;8+* Ce ]lm|ljmkemkýj Dl mojtljkdo} lj Mkljmke} Lrvlpkaljtecl}* @epmlcoje* L}veõe* vv 50>† MPOALP# ECEJ B* "5;;4+Ná}kme vepe ce} Mkljmke} dl ce ^kde* @epmlcoje* Ldkt* Pl~lptë# ]*E* vv*<82*† DEK]B# NLJDLP [ OTPO]…Ná}kme Lrvlpkaljtec * Aërkmo* Ldkt* Bk}vejo Ealpkmejo* vv*=40

† H\LPPE ̂ LCE# MCE\DKO "5;8;+* Aej|ec dl Ce`opetopko dl Ná}kme vepe Ael}tpo}* Aërkmo* Ldkt* Tpkcce}*vv*082*† ALKJLP]# BEPP[ N* "5;26+* Lrvlpkaljto} dl Ná}kme* Aërkmo* Ldkt* Cka|}e ]*E* vv*455† AKJK]TLPKO DL LD\MEMKÝJ"5;;<+* Aej|ec vepe lc |}o dlc aýd|co dl Ná}kme *Ckae# Vlp÷* vv 024*

† XKC]OJ GLPP[ D* "5;;>+ Ná}kme* Aërkmo* Vpljtkml Becc Bk}vejoealpkmeje# ]*E* vv* 88>*

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