I hear a knocking
At the south entry: retire we to our chamber;
A little water clears us of this deed:
How easy is it, then!" -Lady Macbeth (Act 2, Scene 2)

Symbol:
Washing of hands: After Macbeth returns from killing Duncan Lady Macbeth explains to him that by simply washing his hands his sins will vanish. Macbeth believes that no amount of water will erase his guilt but Lady Macbeth assures him that the water will wash away his sins. Soon her hands are just as bloody as Macbeths and she goes to wash away her sins as well and falls for her own deception. The washing of their hands symbolizes washing off their sins and relieving them of guilt. 

Analysis: 
Both of these quotes are discussing or from Lady Macbeth. To me, she is one of the most deceitful characters. In quote 1 we see how Macduff sees through her deceitfulness. She portrays such an innocent and naive front but inside her true self is deceitful and puppet master. In quote two we see connotation from the puppet master herself. Here we see how she is deceiving Macbeth and that he easily falls for her deceit. The strength of her deceitfulness shows how she was the true puppet master behind this murder and convinced Macbeth to get his hands dirty. Even though in the end she had to get her hands dirty as well she still received Macbeth and told him their sins would wash away will water. 

Symbol: Dagger
A vision of a dagger appears to Macbeth in the moments before he enters Duncan's bedroom to kill him. Most likely, this vision of a floating bloody dagger is actually a response to the guilt that Macbeth is feeling, and is not literally floating before him. This dagger symbolizes the murderous deed that Macbeth commits because it is the tool used to commit the crime.The fact that Macbeth comes back to Lady Macbeth with the bloody dagger instead of leaving it with the guards, reflects the guilt that Macbeth carries around with him.

Quote 1: 

"Is this a dagger which I see before me,

The handle toward my hand? Come, let me clutch thee.

I have thee not, and yet I see thee still.

Art thou not, fatal vision, sensible

To feeling as to sight?"

"Our chimneys were blown down and, as they say,

Lamentings heard i' th' air, strange screams of death,

And prophesying with accents terrible

Of dire combustion and confused events

New hatched to the woeful time. The obscure bird

Clamored the livelong night. Some say the Earth

Was feverous and did shake."

In both of these quotes, individuals who have been or will become affected by the death of Duncan experience something "supernatural". Unable to fully process and come to terms with what he is about to do, Macbeth has severe hallucinations of a dagger that he cannot physically grasp. Some of the townspeople report that the air felt "strange" and that the Earth "did shake" even before they knew that Duncan had been killed. The brutal slaying of Duncan's death was so powerful that it created a devilish and maleficent atmosphere that had a powerful effect on those in the town.