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13-Jan-2017
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### Transcript of Διαγώνισμα στα...

• 1

() : 9 2015

(10 M)

1. ; ............................................................................................................ ............................................................................................................ ............................................................................................................

2. ; ............................................................................................................ ............................................................................................................ ............................................................................................................

3. a!, b!, c! ,

: )()( cbacba !!!!!! = .

............................................................................................................

............................................................................................................

...........................................................................................................

4. a!, b!

,

:: a!b!= c!d! a

!

c! = d

!

b!

............................................................................................................

............................................................................................................

............................................................................................................

5. ; ............................................................................................................ ............................................................................................................ ...........................................................................................................

• (10 M)

1. !a = (2015, 2016),

!b = (k, 1) :

.k = 1, . k = 20152016

. k = 20162015

. k = 20152016

, . bak!! =

2. =u! , ( )

., B. , . = , . =

2 ,

E. =

4

3. += xy

v!= 2,( ), "* :

. = 2 , . = 0.5 , . = 2 , . = -0.5 , E.

4. . : . , . x 'x , . y 'y , . ,

.

5. u!, v!

u!= v

!, v

!( ), v! = u! , u!( ) . u!, v! :

. , . , . , . , .

• - (10 M) 1. .

2. 0ba!! , a! b

!

3.

4. .

5.

(10 M)

1. u!, v"! 0

! u

! v

! v

!u!

=

2. ................ .

3. u!= 0, 2 + 2016( )

..................... x 'x 4. .. 5. ),(),4,( == vu !! ,

02 =++ xax

; ............................................................................................................ ............................................................................................................ ............................................................................................................

• (60 M)

1. O 0, 0( ) , B xA , yA( ), B xB , yB( ) . M xM , yM( ) . :

) ! "!!

= ! "!!

+! "!!

2.

)2

2

AM

AM

BB yyyxxx +=+=.

2. xy ,

x 'x ,

x2 2 5 + 20( )x 2016 = 0 ! 7.

3. ,,a

: 0=++

!"

2015=

!"=

!"!"!

2016.

!"

!"

4. u!= 9, 19( ) .

!"= 5, 3( )

!